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## Kerala State Syllabus 6th Standard Maths Solutions Chapter 4 Volume

### Volume Text Book Questions and Answers

Large and small Textbook Page No. 57

Athira has collected many things and has arranged them into different lots.

Look at two things from the first lot.

Which is bigger?

How did you find out?

Now look at two things from the second lot:

How do we find out which is bigger?

To find out the bigger of two sticks, we need only measure their lengths.

What about two rectangles?

We have to calculate their area, right?

Answer:

Yes,

Explanation:

Yes, by calculating the area we can find which of the two envelopes is bigger.

Rectangle blocks

Look at two wooden blocks from Athira’s collection. Which is larger?

How did you decide?

Now look at these two.

Which is larger?

Let’s see how we can decide.

Answer:

The block with more volume is larger,

Explanation:

We can decide about a larger wooden block by comparing their volumes. Volume = length X breadth X height.

Size of a rectangle block Textbook Page No. 59

Look at these rectangular blocks:

They are all made by stacking smaller blocks of the same size.

Which of them is the largest?

We need only count the little blocks in each, right?

Can you find how many little blocks make up each of large blocks below?

Is there a quick way to find the number of little blocks in each, without actually counting all?

Answer:

Yes, we can find the number of little blocks which make up the large block. Yes, there is quick way to find the number of little blocks ; Count the number of blocks in length , breadth and height wise.

By the product of these values we can get the total number of small blocks.

This rectangular block contains 64 smaller blocks. If one small block is removed from each corner of the large block

above, how many would be left?

Answer:

56 small blocks are left,

Explanation:

Total number of small blocks in rectangular block = 64, Number of corners in a rectangular block = 8, Number of small blocks left in the rectangular block = 64 – 8 = 56.

Which of these is the largest?

And the smallest?

Answer:

Second block is larger than the first,

Explanation:

Volume of the first rectangular block = length X breadth X height = 3 X 3 X 3 = 27 cubic units,

Volume of the second rectangular block = length X breadth X height = 5 X 3 X 4 = 60 cubic units,

Therefore, second block is larger than the first.

Look at these blocks:

How many small blocks are there in each?

Do they have the same size?

To compare sizes by just counting, what kind of little blocks should be used in both?

Answer:

Same shape and size,

Explanation:

Each block consists of 12 small blocks. Yes, the two blocks are of same size. The little blocks used should be of same shape and size.

Size as number Textbook Page No. 60

Look at this picture:

What is the area of the rectangle?

How many small squares of side 1 centimetre are in it?

4 X 3 = 12

The area of a square of side 1 centimetre is 1 square centimetre; the area of the whole rectanlge is 12 square centimetres.

Now look at the rectangular block:

It is made by stacking cubes of side 1 centimetre.

How many?

So, the size of this block is equal to 24 such cubes.

Size measured like this is called volume in mathematics.

We say that a cube of length, breadth and height 1 centimetre has a volume of 1 cubic centimetre.

24 such cubes make up the large block in the picture.

Its volume is 24 cubic centimetre.

All sides of the large cube shown above are painted. How many small cubes would have no paint at all?

Answer:

One cube is left,

Explanation:

Only one cube is left with no paint on it which is in the middle of the large cube.

All blocks shown below are made up of cubes of side 1 centimetre. Calculate the volume of each:

Answer:

64 cubic centimetres,12 cubic centimetres,64 cubic centimetres,36 cubic centimetres,63 cubic centimetres,12 cubic centimetres,

Explanation:

Total number of cubes = length X breadth X height = 4 X 4 X 4 = 64, if side of each small cube is 1 centimetre then Volume of each small cube = length X breadth X height = 1 X 1 X 1 = 1 cubic centimetres, Therefore volume of the figure = total number of cubes X volume of each small cube = 64 cubic centimetres.

Total number of cubes = length X breadth X height = 2 X 2 X 3 = 12, if side of each small cube is 1 centimetre then

Volume of each small cube = length X breadth X height = 1 X 1 X 1 = 1 cubic centimetres, Therefore volume of the figure = total number of cubes X volume of each small cube = 12 cubic centimetres.

Total number of cubes = length X breadth X height = 4 X 4 X 4 = 64, if side of each small cube is 1 centimetre then

Volume of each small cube = length X breadth X height = 1 X 1 X 1 = 1 cubic centimetres, Therefore volume of the figure = total number of cubes X volume of each small cube = 64 cubic centimetres.

Total number of cubes = length X breadth X height = 4 X 3 X 3 = 36, if side of each small cube is 1 centimetre then

Volume of each small cube = length X breadth X height = 1 X 1 X 1 = 1 cubic centimetres, Therefore volume of the figure = total number of cubes X volume of each small cube = 36 cubic centimetres.

Total number of cubes = length X breadth X height = 7 X 3 X 3 = 63, if side of each small cube is 1 centimetre then

Volume of each small cube = length X breadth X height = 1 X 1 X 1 = 1 cubic centimetres, Therefore volume of the figure = total number of cubes X volume of each small cube = 63 cubic centimetres.

Total number of cubes = length X breadth X height = 2 X 3 X 2 = 12, if side of each small cube is 1 centimetre then

Volume of each small cube = length X breadth X height = 1 X 1 X 1 = 1 cubic centimetres, Therefore volume of the figure = total number of cubes X volume of each small cube = 12 cubic centimetres.

Volume calculation Textbook Page No. 62

See this rectangular block:

How do we calculate its volume?

Answer:

Volume is 15 cubic centimetre,

Explanation:

Volume of the rectangular block = length X breadth X height = 5 X 3 X 1 = 15 cubic centimetre.

Therefore, it’s volume is 15 cubic centimetre.

For that, we must find out how many cubes of side 1 centimetre we need to make it.

So, its volume is 15 cubic centimetres.

What about this block?

This can be made by stacking one over another, two blocks seen first:

So, to make it, how many cubes of side 1 centimetre do we need?

Thus the volume of this block is 30 cubic centimetres.

Like this, calculate the volume of each of the rectangular blocks shown below and write it beside each:

Answer:

1) 56 cubic centimetres,

2) 54 cubic centimetres,

3) 125 cubic centimetres,

4) 100 cubic centimetres,

Explanation:

1) Length = 7 centimetres, Breadth = 4 centimetres, Height = 2 centimetres,

Volume of the rectangular block = length X breadth X height = 7 X 4 X 2 = 56 cubic centimetres.

2) Length = 6 centimetres, Breadth = 3 centimetres, Height = 3 centimetres

Volume of the rectangular block = length X breadth X height = 6 X 3 X 3 = 54 cubic centimetres.

3) Length = 5 centimetres, Breadth = 5 centimetres, Height = 5 centimetres,

Volume of the rectangular block = length X breadth X height = 5 X 5 X 5 = 125 cubic centimetres.

4) Length = 5 centimetres, Breadth = 4 centimetres, Height = 5 centimetres

Volume of the rectangular block = length X breadth X height = 5 X 4 X 5 = 100 cubic centimetres.

So, now, you know how to calculate the volume of a rectangular block, dont’ you?

The volume of a rectangular block is the product of its length, breadth and height.

Question 1.

The length, breadth and height of a brick are 21 centimetres, 15 centimetres and 7 centimetres. What is its volume?

Answer:

Volume is 2205 cubic centimetres,

Explanation:

Volume of the rectangular block = length X breadth X height = 21 X 15 X 7 = 2,205 cubic centimetres.

Question 2.

A rectangular cube of iron is of side 8 centimetres. What is its volume? 1 cubic centimetre of iron weighs 8 grams. What is the weight of the large cube?

Answer:

Weight of large cube is 4096 grams,

Explanation:

Volume of a rectangular cube = side X side X side = 8 X 8 X 8 = 512 cubic centimetres, Weight of 1 cubic centimetre of iron = 8 grams, Weight of the large cube = 512 cubic centimetres X 8 grams = 4,096 grams, Therefore, weight of the large cube is 4,096 grams or 4.096 kilo grams.

Volume and length Textbook Page No. 65

A wooden block of length 8 centimetres and breadth 4 centimetres has a volume of 180 cubic centimetres. What is its height?

Volume is the product of length, breadth and height.

So in this problem, the product of 9 and 4 multiplied by the height is 180.

That is, 36 multiplied by the height gives 180.

So to find out the height, we need only divide 180 by 36.

The table shows measurement of some rectangular blocks. Calculate the missing measures.

Answer:

Explanation:

1) Length = 3 centimetres, Breadth = 8 centimetres, Height = 7 centimetres,

Volume of the rectangular block = length X breadth X height = 3 X 8 X 7 = 168 cubic centimetres.

2)Length = 6 centimetres, Breadth = 4 centimetres, Height = 5 centimetres,

Volume of the rectangular block = length X breadth X height = 6 X 4 X 5 = 120 cubic centimetres.

3)Length = 6 centimetres, Breadth = 4 centimetres, Volume of the rectangular block = length X breadth X height = 6 X 4 X height = 48 cubic centimetres , Height = \(\frac{48}{24}\) = 2 centimetres.

4)Length = 8 centimetres, Height = 2 centimetres, Volume of the rectangular block = length X breadth X height = 8 X breadth X 2 = 48 cubic centimetres, Breadth = \(\frac{48}{16}\) = 3 centimetres.

5) Breadth = 2 centimetres, Height = 2 centimetres, Volume of the rectangular block = length X breadth X height = length X 2 X 2 = 48 cubic centimetres, Length = \(\frac{48}{4}\) = 12 centimetres.

6) Breadth = 2 centimetres, Height = 4 centimetres, Volume of the rectangular block = length X breadth X height = length X 2 X 4 = 80 cubic centimetres, Length = \(\frac{80}{8}\) = 10 centimetres.

7)Length = 14 centimetres, Height = 5 centimetres, Volume of the rectangular block = length X breadth X height = 14 X breadth X 5 = 210 cubic centimetres, Breadth = \(\frac{210}{70}\) = 3 centimetres.

Area and volume

What is the area of a rectangle of length 8 centimetres and breadth 2 centimetres?

What about the volume of a rectangular block of length 8 centimetres, breadth 2 centimetres and height 1 centimetre?

Answer:

Area is 16 square centimetres, Volume is 16 cubic centimetres,

Explanation:

Length= 8 centimetres, Breadth= 2 centimetres, Height= 1 centimetre. Area of rectangle = length X breadth = 8 X 2 = 16 square centimetres, Volume of rectangle = length X breadth X height = 8 X 2 X 1 = 16 cubic centimetres.

New shapes Textbook Page No. 66

We can make shapes other than rectangular block, by stacking cubes. For example, see this:

It is made by stacking cubes of side I centimetre. Can you calculate its volume?

How many cubes are there at the very bottom?

And in the step just above it?

Thus we can count the number of cubes in each step.

How many cubes in all?

What is the volume of the stairs?

Answer:

Volume of the stairs is 216 cubic centimetres,

Explanation:

Yes, we can calculate the volume of the given figure. There are total of 81 cubes in the bottom line because there are 9 cubes vertically and 9 cubes horizontally arranged product of these gives the number of cubes. There are total of 63 cubes in the bottom line because there are 7 cubes vertically and 9 cubes horizontally arranged product of these gives the number of cubes.

There are total of 216 cubes in the given figure obtained by adding the cubes of each line.

Volume of the stairs = total number of cubes ( since 1 cube is of 1 cubic centimetre in volume ) = 81 + 63 + 45 + 27 = 216 cubic centimetre.

Now look at this figure:

It is made by stacking square blocks. The bottom block is of side 9 centimetres. As we move up, the sides decrease by 2 centimetres at each step.

What is the volume of a rectangular block of length 4 centimetre, breadth 3 centimetre and

height 1 centimetre? If the length, breadth and height are doubled, what happens to the volume?

Answer:

Volume of rectangular block is 12 cubic centimetres. If the length, breadth and height of a rectangular block are doubled then the volume increases by 8 times.

Explanation:

Length = 4 centimetre, Breadth = 3 centimetre, Height = 1 centimetre,

Volume of rectangular block = length X breadth X height = 4 X 3 X 1 = 12 cubic centimetres.

If the length, breadth and height are doubled then Length = 8 centimetre, Breadth = 6 centimetre

Height = 2 centimetre,Volume of rectangular block = length X breadth X height = 8 X 6 X 2 = 96 cubic centimetres.

Therefore, if the length, breadth and height of a rectangular block are doubled then the volume increases by 8 times.

All blocks are of height 1 centimetre. What is the volume of this tower?

Just calculate the volume of each square block and add. Try it!

Answer:

Volume of the tower is 165 cubic centimetres,

Explanation:

Length = 9 centimetre, Breadth = 9 centimetre, Height = 1 centimetre, Volume of first square block = length X breadth X height = 9 X 9 X 1 = 81 cubic centimetres.

Length = 7 centimetre, Breadth = 7 centimetre , Height = 1 centimetre, Volume of second square block = length X breadth X height = 7 X 7 X 1 = 49 cubic centimetres.

Length = 5 centimetre, Breadth = 5 centimetre, Height = 1 centimetre, Volume of third square block = length X breadth X height = 5 X 5 X 1 = 25 cubic centimetres.

Length = 3 centimetre, Breadth = 3 centimetre, Height = 1 centimetre, Volume of fourth square block = length X breadth X height = 3 X 3 X 1 = 9 cubic centimetres.

Length = 1 centimetre, Breadth = 1 centimetre, Height = 1 centimetre, Volume of fifth square block = length X breadth X height = 1 X 1 X 1 = 1 cubic centimetres. Volume of the tower = 81 + 49 + 25 + 9 + 1 = 165 cubic centimetres.

Calculate the volumes of the figures shown below. All lengths are in centimetres.

Answer:

1) 416 cubic centimetres, 2) 448 cubic centimetres, 3) 324 cubic centimetres,

Explanation:

1) Volume of the given figure = Volume of vertical cuboid + Volume of horizontal cuboid + Volume of horizontal cuboid + Volume of cube, Length = 20 centimetre, Breadth = 4 centimetre, Height = 2 centimetre, Volume of vertical cuboid = length X breadth X height = 20 X 4 X 2 = 160 cubic centimetres, Length = 12 centimetre, Breadth = 4 centimetre, Height = 2 centimetre, Volume of horizontal cuboid = length X breadth X height = 12 X 4 X 2 = 96 cubic centimetres, Length of side of cube = 4 centimetres, Volume of cube = side X side X side = 4 X 4 X 4 = 64 cubic centimetres, Volume of the given figure = 160 cubic centimetres + 96 cubic centimetres + 96 cubic centimetres + 64 cubic centimetres = 416 cubic centimetres.

2) Volume of the given figure = Volume of vertical cuboid + Volume of vertical cuboid + Volume of cube, Length = 16 centimetre, Breadth = 4 centimetre, Height = 3 centimetre, Volume of vertical cuboid = length X breadth X height = 16 X 4 X 3 = 192 cubic centimetres, Length of side of cube = 4 centimetres, Volume of cube = side X side X side = 4 X 4 X 4 = 64 cubic centimetres, Volume of the given figure = 192 cubic centimetres + 192 cubic centimetres + 64 cubic centimetres = 448 cubic centimetres.

3) Volume of the given figure = Volume of vertical cuboid + Volume of horizontal cuboid, Length = 11 centimetre, Breadth = 4 centimetre, Height = 3 centimetre, Volume of vertical cuboid = length X breadth X height = 11 X 4 X 3 = 132 cubic centimetres, Length = 16 centimetre, Breadth = 4 centimetre, Height =3 centimetre, Volume of horizontal cuboid = length X breadth X height = 16 X 4 X 3 = 192 cubic centimetres, Volume of the given figure = 132 cubic centimetres + 192 cubic centimetres = 324 cubic centimetres.

Large measures Textbook Page No. 67

What is the volume of a cube of side 1 metre?

I metre means 100 centimetres?

So, we must calculate the volume of a cube of side 100 centimetres. How much is it?

We say that the volume of cube of 1 metre is 1 cubic metre.

So,

1 cubic metre = 1000000 cubic centimetre.

Volume of large objects are often said as cubic metres.

Question 1.

A truck is loaded with sand, 4 metre long, 2 metre wide and 1 metre high. The price of 1 cubic metre of sand is 1000

rupees. What is the price of this truck load?

Answer:

Price of the truck loaded with sand is 8000 rupees,

Explanation:

Volume of the truck loaded with sand =length X breadth X height = 4 X 2 X 1 = 8 cubic metres.

Price of 1 cubic metre of sand = 1000 rupees, Price of the truck loaded with sand = 8 cubic metres X 1000 rupees = 8000 rupees, Therefore, price of the truck loaded with sand is 8000 rupees.

Question 2.

What is the volume in cubic metres of a platform 6 metre long, 1 metre wide and 50 centimetre high?

Answer:

Volume of the rectangular block is 3 cubic metres,

Explanation:

Length = 6 metre, Breadth = 1 metre, Height = 50 cm = \(\frac{1}{2}\) metre, Volume of the rectangular block = length X breadth X height = 6 X 1 X \(\frac{1}{2}\) = 3 cubic metres.

Question 3.

What is the volume of a piece of wood which is 4 metres long, \(\frac{1}{2}\) metre wide and 25 centimetre high? The price of 1 cubic metre of wood is 60000 rupees. What is the price of this piece of wood?

Answer:

Price of the piece of wood is 30,000 rupees,

Explanation:

Length = 4 metre, Breadth = \(\frac{1}{2}\) metre, Height = 25 cm = \(\frac{1}{4}\) metre,

Volume of a piece of wood = length X breadth X height = 4 X \(\frac{1}{2}\) X \(\frac{1}{4}\) = \(\frac{1}{2}\) cubic metre, Price of 1 cubic metre of wood = 60000 rupees, Price of the piece of wood = \(\frac{1}{2}\) cubic metre X 60000 rupees = 30000 rupees, Therefore, price of the piece of wood is 30,000 rupees.

Capacity

Look at this hollow box:

It is made with thick wooden planks. Because of the thickness, its inner length, breadth and height are less than the outer measurements.

The inner length, breadth and height are 40 centimetres, 20 centimetres and 10 centimetres.

So, a rectangular block of these measurement can exactly fit into the space within this box.

The volume of this rectangular block is the volume whithin the box.

This volume is called the capacity of the box.

Thus the capacity of this box is;

40 X 20 X 10 = 8000 cc

So, what is the capacity of a box whose inner length, breadth and height are 50 centimetres, 25 centimetres and 20 centimetres?

Answer:

Capacity of the box is 25,000 cubic centimetres,

Explanation:

Length = 50 centimetres, Breadth = 25 centimetres, Height = 20 centimetres, Thus the capacity of the box = 50 X 25 X 20 = 25,000 cubic centimetres.

Litre and cubic metre

1 litre is 1000 cubic centimetres and 1 cubic metres is 1000000 cubic centimetres. So, 1 cubic metre is 1000 litres.

Liquid measures

What is the capacity of a cubical vessel of inner side 10 centimetres?

10 × 10 × 10 = 1000 cubic centimetres

1 litre is the amount of water that fills this vessel.

That is

1 litre = 1000 cubic centimetres

We can look at this in another way. Ifa cube of side 10 centimetres in completely immersed in a vessel, filled with water then the amount of water that overflows would be 1 litre.

So, how many litres of water does if a vessel of length 2 centimetres, breadth 15 centimetres and height 10 centimetres contain?

Let’s look at another problem:

A rectangular tank of length 4 metres and height 2\(\frac{1}{2}\) metres can contain 15000 litres of water. What is the breadth of the tank?

If we find the product of length, breadth and height in metres. we get the volume in cubic metres.

Here the volume is given to be 15000 litres.

That is, 15 cubic metres.

The product of length and height is

4 X 2\(\frac{1}{2}\) = 10

So, breadth multiplied by 10 is 15.

From this, we can calculate the width as \(\frac{15}{10}\) = 1\(\frac{1}{2}\) metre.

Now suppose this tank contains 6000 litres of water. What is the height of the water?

The amount of water is 6 cubic metres. So, the product of the length and breadth of the tank and the height of the water, all in metres is 6.

Product of length and breadth is; 4 X 1\(\frac{1}{2}\) = 6

So, height is 6 ÷ 6 = 1 metre.

In the water Textbook Page No. 69

A vessel is filled with water. If a cube of side 1 centimetre is immersed into it, how many cubic centimetre of water would overflow? What if 20 such cubes are immersed?

Answer:

If 1 cube is immersed then 1 cubic centimetre of water would overflow, If 20 cubes are immersed then 20 cubic centimetre of water would overflow,

Explanation:

Volume of the object added in the vessel = Volume of water displaced or overflowed, Volume of 1 small cube = side X side X side = 1 X 1 X 1 = 1 cubic centimetre. Therefore, 1 cubic centimetre of water were overflowed. Volume of 20 small cube = 20 (Volume of 1 small cube ) = 20 (side X side X side) = 20 (1 X 1 X 1) = 20 cubic centimetres. Therefore, 20 cubic centimetres of water were overflowed.

Raising water

A swimming pool is 25 metres long, 10 metres wide and 2 metre deep. It is half filled. How many litres of water does it contain now?

25 × 10 × 1 = 250 cubic metres

= 250000 litre

Suppose the water level is increased by 1 centimetre. How many more litres of water does it contain now?

Answer:

25,2500 litres of water will be increased in the swimming pool,

Water level is increased by 1 centimetre, Length = 25 metres, Breadth = 10 metres, Height = 2.01 metres, Volume of swimming pool = length X breadth X height = 25 X 10 X 2.01 = 502.5 cubic metres = 502500 litres, Number of more litres of water to be added = Volume of swimming pool after increasing 1 centimetres – Volume of swimming pool = 502500 litres – 250000 litres = 25,2500 litres.

Textbook Page No. 70

Question 1.

The inner sides of a cubical box are of length 4 centimetres. What is its capacity? How many cubes of side 2 centimetres can be stacked inside it?

Answer:

8 cubes can be stacked inside the cubical box,

Explanation:

Length = 4 centimetres, Volume of inner sides of a cubical box = length X length X length = 4 X 4 X 4 = 64 cubic centimetres. If side = 2 centimetres, Volume of the cube = side X side X side = 2 X 2 X 2 = 8 cubic centimetres, Cubes stacked inside the cubical box = \(\frac{Volume of inner sides of a cubical box}{Volume of the cube}\) = \(\frac{64}{8}\) = 8 cubes.

Question 2.

The inner side of a rectangular tank are 70 centimetres, 80 centimetres, 90 centimetres. How many litres of

water can it contain?

Answer:

504 litres of water are in the rectangular tank,

Explanation:

Length = 70 centimetres, Breadth = 80 centimetres, Height = 90 centimetres, Capacity of the rectangular tank = 70 X 80 X 90 = 504000 cubic centimetres = 0.504 cubic metres = 504 litres ( since 1 cubic metre = 1000 litres).

Question 3.

The length and breadth of a rectangular box are 90 centimetres and 40 centimetres. It contains 180 litres of water. How high is the water level?

Answer:

Height of the rectangular box is 50 centimetres,

Explanation:

Length = 90 centimetres, Breadth = 40 centimetres, Capacity of the rectangular box = 180 litres = 180000 cubic centimetres ( since 1 cubic centimetre= 0.001 litre), Volume of the rectangular box = Capacity of rectangular box = length X breadth X height = 90 X 40 X height = 180000 cubic centimetres, Product of length and breadth = 90 X 40 = 3600 square centimetres, Height of the rectangular box = \(\frac{180000}{3600}\) = 50 centimetres.

Question 4.

The inner length, breadth and height of a tank are 80 centimetres, 60 centimetres and 15 centimetres, and it contains water 15 centimetre high. How much more water is needed to fill it?

Answer:

The tank is already filled with 72 litres because the tank is filled 15 centimetres high,

Explanation:

Length = 80 centimetres, Breadth = 60 centimetres, Height = 15 centimetres, Capacity of the rectangular tank = 80 X 60 X 15 = 72000 cubic centimetres = 0.072 cubic metres = 72 litres ( since 1 cubic metre = 1000 litres).

Question 5.

The panchayat decided to make a rectangular pond. The length, breadth and depth were decided to be 20 metres, 15 metres and 2 metres. The soil dug out was removed in a truck which can cariy a load of length 3 metres, breadth 2 metres and height 1 metre. How many truck loads of soil have to be moved?

Answer:

100 loads of soil have to be moved in the truck to form a rectangular pond,

Explanation:

Length = 20 metres, Breadth = 15 metres, Height = 2 metres, Volume of the rectangular pond = length X breadth X height = 20 X 15 X 2 = 600 cubic metres. If dimensions of truck are : Length = 3 metres, Breadth = 2 metres, Height = 1 metres, Volume of sand loaded in truck = length X breadth X height = 3 X 2 X 1 = 6 cubic metres. Number of truck loads of soil = \(\frac{Volume of the rectangular pond }{Volume of sand loaded in truck}\) = \(\frac{600}{6}\) = 100 loads.

Question 6.

The inner length and breadth of an aquarium are 60 centimetres and 30 centimetres. It is half filled with water. When a stone is immersed in it, the water level rose by 10 centimetres. What is the volume of the stone?

Answer:

Volume of the stone is 18,000 cubic centimetres,

Explanation:

Length = 60 centimetres, Breadth = 30 centimetres, Height = h centimetres, Volume of the aquarium = length X breadth X height = 60 X 30 X h = 1800 h cubic centimetres. After immersing a stone then Length = 60 centimetres, Breadth = 30 centimetres, Height = (h+10) centimetres, Volume of the aquarium after adding a stone = length X breadth X height = 60 X 30 X (h+10) = 1800 (h+10) cubic centimetres, Volume of the stone = Volume of the aquarium after adding a stone – Volume of the aquarium = 1800 (h+10) – 1800 = 1800 h + 18000 – 1800 h = 18000 cubic centimetres.

Question 7.

A rectangular iron block has height 20 centimetres, breadth 10 centimetres and height 5 centimetres. It is melt and recast into a cube. What is the length of a side of this cube?

Answer:

Length of side of the cube is 10 centimetres,

Explanation:

Length = 20 centimetres, Breadth = 10 centimetres, Height = 5 centimetres,

Volume of the rectangular iron block = length X breadth X height = 20 X 10 X 5 = 1000 cubic centimetres, The rectangular iron box is recast into a cube. Volume of the cube = Volume of the rectangular box = 1000 cubic centimetres, side X side X side = 1000 cubic centimetres, side of cube = 10 centimetres.

Question 8.

A tank 2\(\frac{1}{2}\) metre long and 1 metre wide is to contain 10000 litres. How high must be the tank?

Answer:

Height of the tank is 4 metres,

Explanation:

Length = 2.5 metres, Breadth = 1 metre, Capacity of the tank = 10000 litres =10 cubic metres ( since 1 cubic metre= 1000 litre), Volume of the tank = Capacity of the tank = length X breadth X height = 2.5 X 1 X height = 10 cubic metres, Product of length and breadth = 2.5 X 1 = 2.5 square metres, Height of the tank = 10 / 2.5 = 4 metres.

Question 9.

From the four corners of a square piece of paper of side 12 centimetres, small squares of side 1 centimetre are cut

off. The edges of this are bent up and joined to form a container of height 1 centimetre. What is the capacity of the container? If squares of side 2 centimetres are cut off, what would be the capacity?

Answer:

Capacity of the container is 100 cubic centimetres, The capacity of square piece after cut off of squares is 84 cubic centimetres,

Explanation:

Dimensions of container are: Length = 12 – 1 – 1 = 10 centimetres, Breadth = 12 – 1 – 1 = 10 centimetres, Height = 1 centimetre, Capacity of the container = length X breadth X height = 10 X 10 X 1 = 100 cubic centimetres, If side of square = 2 centimetres, Capacity of the square = length X breadth X height = 2 X 2 X 1 = 4 cubic centimetres. Capacity of the square piece after cut off of squares = Capacity of the container – 4 (Capacity of the square) = 100 – 4(4) = 84 cubic centimetres.