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SCERT Class 6 Maths Chapter 3 Solutions Volume
Class 6 Kerala Syllabus Maths Solutions Chapter 3 Volume Questions and Answers
Volume Class 6 Questions and Answers Kerala Syllabus
Size as Number (Page No. 37)
Question 1.
All blocks shown below are made up of cubes of side 1 centimetre. Calculate the violume of each.
Answer:
Figure 1
Length = 4 small cube = 4 cm
Width = 4 small cube = 4 cm
Height = 4 small cube = 4 cm
Therefore volume = 4 × 4 × 4 = 64 cubic cm
Figure 2
Length = 2 small cube = 2 cm
Width = 2 small cube = 2 cm
Height = 3 small cube = 3 cm
Therefore volume = 2 × 2 × 3 = 12 cubic cm
Figure 3
Length = 4 small cube = 4 cm
Width = 3 small cube = 3 cm
Height = 3 small cube = 3 cm
Therefore volume = 4 × 3 × 3 = 36 cubic cm
Figure 4
Length = 7 small cube = 7 cm
Width = 2 small cube = 2 cm
Height = 3 small cube = 3 cm
Therefore volume = 7 × 2 × 3 = 42 cubic cm
Figure 5
Length = 3 small cube = 3 cm
Width = 2 small cube = 2 cm
Height = 2 small cube = 2 cm
Therefore volume = 3 × 2 × 2 = 12 cubic cm
Intext Questions (Page No. 40)
Question 1.
Calculate the volume of each of the rectangular blocks shown below:
Answer:
Figure 1
Length = 7 small cube = 7 cm
Width = 4 small cube = 4 cm
Height = 1 small cube = 1 cm
Therefore volume = length × width × height
= 7 × 4 × 1
= 28 cubic cm
Figure 2
Length = 6 small cube = 6 cm
Width = 3 small cube = 3 cm
Height = 3 small cube = 3 cm
Therefore volume = length × width × height
= 6 × 3 × 3
= 54 cubic cm
Figure 3
Length = 5 small cube = 5 cm
Width = 5 small cube = 5 cm
Height = 5 small cube = 5 cm
Therefore volume = length × width × height
= 5 × 5 × 5
= 125 cubic cm
Figure 4
Length = 5 small cube = 5 cm
Width = 4 small cube = 4 cm
Height = 5 small cube = 5 cm
Therefore volume = length × width × height
= 5 × 4 × 5
= 100 cubic cm
Volume Calculation (Page No. 40)
Question 1.
The length, width, and height of a brick are 21 centimetres, 15 centimetres, and 7 centimetres. What is its volume?
Answer:
Length of a brick = 21 cm
Width = 15 cm
Height = 7 cm
Volume = 21 × 15 × 7
= 315 × 7
= 2205 cubic cm
Question 2.
An iron cube is of side 8 centimetres. What is its volume? 1 cubic centimetre of iron weighs 8 grams. What is the weight of this cube?
Answer:
Volume = 8 × 8 × 8 = 512 cubic cm.
Weight of this cube = 512 × 8 = 4096 cubic cm
Volume and Length (Page No. 41)
Question 1.
The table shows the measurements of some rectangular blocks. Calculate the missing measures.
Answer:
New Shapes (Page No. 42)
Question 1.
Calculate the volumes of the shapes shown below. All lengths are in centimetres.
Answer:
Figure 1
(i) 8 × 4 × 2 = 64 cubic cm.
(ii) 8 × 4 × 2 = 64 cubic cm.
(iii) 20 × 4 × 2 = 160 cubic cm.
(iv) 4 × 4 × 2 = 32 cubic cm.
Total volume = 64 + 64 + 160 + 32 = 320 cubic cm.
Figure 2
(i) 16 × 3 × 4 = 192 cubic cm.
(ii) 16 × 3 × 4 = 192 cubic cm.
(iii) 4 × 3 × 4 = 48 cubic cm.
Total volume = 192 + 192 + 48 = 432 cubic cm.
Figure 3
(i) 16 × 3 × 4 = 192 cubic cm.
(ii) 11 × 3 × 4 = 132 cubic cm.
Total volume = 192 + 132 = 324 cubic cm
Large Measures (Page No. 43)
Question 1.
A truck is loaded with sand, 4 metres long, 2 metres wide, and 1 metre high. The price of 1 cubic metre of sand is 1000 rupees. What is the price of this truckload?
Answer:
Volume of the truck = 4 × 2 × 1 = 8 cubic metre
The price of 1 cubic metre of sand = 1000 rupees.
The price of 8 cubic metre sand = 8 × 1000 = 8000 rupees
Question 2.
What is the volume in cubic centimetres of a platform 6 metres long, 1 metre wide, and 50 centimetres high?
Answer:
Volume of the platform = 6 m × 1 m × 50 cm
= 600 × 100 × 50
= 3,000,000 cubic cm
Question 3.
What is the volume of a piece of wood that is 5 metres long, 1 metre wide, and 25 centimetres high? The price of 1 cubic metre of wood is 60000 rupees. What is the price of this piece of wood?
Answer:
Volume of apiece of wood = 5 m × 1 m × 25 cm
= 500 cm × 100 cm × 25 cm
= 1250000 cubic cm
= 1250000 ÷ 1000000
= 1 cubic metre 250000 cubic cm
= 1\(\frac {1}{4}\) cubic metre
The price of 1 cubic metre of wood = 60000 rupees.
The price of \(\frac {1}{4}\) cubic metre of wood = 15000 rupees.
Therefore the total price = 60000 + 15000 = 75000 rupees
Capacity & Liquid Measures (Page No. 45)
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:
Inner length of the cubical box = 4 cm
Capacity of the box = 4 × 4 × 4 = 64 cubic cm.
Volume of one small cube = 2 × 2 × 2 = 8 cubic cm.
Number of small cubes that can fit inside = 64 ÷ 8 = 8 cubes
Question 2.
The inner sides of a rectangular tank are 70 centimetres, 80 centimetres, and 90 centimetres. How many litres of water can it contain?
Answer:
Capacity of the water tank = 70 × 80 × 90
= 504000 cubic cm
= 504 litres (Since 1000 cubic cm = 1 liter)
Question 3.
The length and width of a rectangular box are 90 centimetres and 40 centimetres. It contains 180 litres of water. How high is the water level?
Answer:
1 litre = 1000 cubic cm.
180 litres = 180 × 1000 = 180,000 cubic cm.
Volume = length × width × height
180,000 = 90 × 40 × height
height = 180,000 ÷ (90 × 40) = 50 cm
Question 4.
The inner length, width, and height of a tank are 80 centimetres, 60 centimetres, and 50 centimetres, and it contains water 15 centimetres high. How much more water is needed to fill it?
Answer:
Inner dimensions of the tank:
Length = 80 cm
Width = 60 cm
Height = 50 cm
Current water height = 15 cm
Capacity of the tank,
Total volume = 80 × 60 × 50 = 240,000 cubic cm.
Capacity = 240 litres
Volume of the water already in the tank = 80 × 60 × 15 = 72,000 cubic cm
Current Capacity = 72 litres
Remaining water needed = 240 – 72 = 168 litres
Or
Now the water is at 15 cm height, and the remaining height is 35 cm.
The water can fill in the remaining portion = 80 × 60 × 35
= 168,000 millilitres
= 168 litres
Question 5.
The panchayat decided to make a rectangular pond. The length, width, and depth were decided to be 20 metres, 15 metres, and 2 metres. How many litres of water are needed to fill this pond to a height of one and a half metres?
Answer:
Length = 20 m = 2000 cm
Width = 15 m = 1500 cm
Height = 1\(\frac {1}{2}\) m = 150 cm
Volume = 2000 × 1500 × 150 = 450,000,000 cubic cm.
= 450 cubic metres
= 450000 litre
Or
Volume = 20 × 15 × 1\(\frac {1}{2}\)
= 300 × 1\(\frac {1}{2}\)
= 300 + 150
= 450 cubic metres
= 450000 litre
Question 6.
The inner length and width 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 rises by 10 centimetres. What is the volume of the stone?
Answer:
When a stone is immersed in the aquarium, the water level rises by 10 centimetres
Volume of the water roses = length × width × 10 cm
= 60 × 30 × 10
= 18000 cubic metres.
Volume of the stone = 18000 cubic cm.
Question 7.
A rectangular iron block has a length of 20 centimetres, a width of 10 centimetres, and a height of 5 centimetres. It is melted and recast into a cube. What is the length of a side of this cube?
Answer:
Volume = 20 × 10 × 5 = 1000 cubic cm
The side of the cube = 10 cm
10 × 10 × 10 = 1000 cubic cm
Question 8.
A tank 2 metres long and 1 metre wide is to contain 10000 litres of water. What should be the height of the tank?
Answer:
1 cubic metre = 1000 litres
10,000 litres = 10 cubic metres
Volume = length × width × height
10 = 2 × 1 × height
height = 10 ÷ (2 × 1)
= 10 ÷ 2
= 5 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 this container? If squares of side 2 centimetres are cut off. What would be the capacity?
Answer:
Original side of the square = 12 cm
After cutting 1 cm from each corner, the length and width were reduced by 2 cm (1 cm from each end)
New length = 12 – 2 = 10 cm
New width = 12 – 2 = 10 cm
Height = 1 cm
Capacity = 10 × 10 × 1 = 100 cubic cm.
If 2 cm is cut off from each side,
New length = 12 – 4 = 8 cm
New width = 12 – 4 = 8 cm
Height = 2 cm
Volume = 8 × 8 × 2 = 128 cubic cm.
Class 6 Maths Chapter 3 Kerala Syllabus Volume Questions and Answers
Class 6 Maths Volume Questions and Answers
Question 1.
Which of the following rectangular blocks has a volume of 30 cubic centimetres?
(a) 3 cm, 4 cm, 5 cm
(b) 5 cm, 3 cm, 2 cm
(c) 4 cm, 7 cm, 2 cm
(d) 10 cm, 2 cm, 2 cm
Answer:
(b) 5 cm, 3 cm, 2 cm
Volume = 5 × 3 × 2 = 30 cubic cm.
Question 2.
Which of the following is correct for the volume of a rectangular block?
(a) Volume is the product of its length and height.
(b) Unit of volume is the square centimetre.
(c) If the length of a rectangular block is doubled, then its volume is also doubled.
(d) 100 cubic centimetres is equal to 1 cubic metre.
Answer:
(a) False.
Reason: volume = length × width × height
(b) False.
Reason: unit of volume is cubic centimetre or cubic metre.
(c) If the length of a rectangular block is doubled, then its volume is also doubled.
(d) False.
Reason: 1000 cubic centimetres is 1 litre
100 cubic centimetres is 100 millilitres.
Question 3.
Match the following:
(a) 1000 cubic centimetre – 10 litre
(b) 1000000 cubic centimetre – 1 millilitre
(c) 1 cubic centimetre – 1 cubic metre
(d) 10000 millilitre – 1 litre
Ans:
(a) 1000 cubic centimetre – 1 litre
(b) 1000000 cubic centimetre – 1 cubic metre
(c) 1 cubic centimetre – 1 millilitre
(d) 10000 millilitre – 10 litre
Question 4.
Find the volume of the rectangular block whose length is 12 centimetres, width is 6 centimetres, and height is 4 centimetres.
Answer:
Volume = 12 × 6 × 4 = 288 cubic centimetres
Question 5.
A rectangular block of length 50 centimetres and width 20 centimetres has a volume of 3000 cubic centimetres. What is the height of the rectangular block?
Answer:
Volume = length × width × height
3000 = 50 × 20 × height
height = 3000 ÷ (50 × 20)
= 3000 ÷ 1000
= 3 cm
Question 6.
A wooden block of length 15 metres, width 4 metres, and height 2 metres. What is its volume?
Answer:
Volume of the wodden block = 15 × 4 × 2 = 120 cubic metres
Question 7.
A tank 4 metres long and 2 metres wide is to contain 16000 litres of water. What should be the height of the tank?
Answer:
Volume = 16000 litre = 16 cubic metre
Volume = length × width × height
16 = 4 × 2 × height
height = 16 ÷ (4 × 2)
= 16 ÷ 8
= 2 metres
Question 8.
Complete the following given below:
(a) 180 cubic metre = _____________ litre
(b) 3000 cubic centimetre = _____________ litre
(c) 2000 litre = _____________ cubic metre
(d) 15 cubic centimetre = _____________ millilitre
(e) 75 cubic metre = _____________ litre
Answer:
(a) 180 cubic metre = 180,000 litre
(b) 3000 cubic centimetre = 3 litre
(c) 2000 litres = 2 cubic metres
(d) 15 cubic centimetre = 15 millilitre
(e) 75 cubic metre = 75,000 litre
Class 6 Maths Chapter 3 Notes Kerala Syllabus Volume
→ To compare the size of two rectangular blocks, we must consider their length, width, and height.
→ The volume of a rectangular block can be calculated by multiplying its length, width, and height.
→ If the measurements are in centimetres, then the volume will be in cubic centimetres.
→ If measurements are in metres, then the volume should be in cubic metres.
→ The volume of a rectangular block is the product of its length, width, and height.
→ For a rectangular block,
- If the length is doubled, the volume becomes twice.
- If the length and width are doubled, the volume becomes four times.
- If the length, width, and height are all doubled, the volume becomes eight times.
→ The volume of a rectangular block is 1 cubic metre if its length is 1 metre, width is 1 metre, and height is 1 metre.
→ 1 cubic metre = 100 × 100 × 100 = 1000000 cubic centimetre
→ The volume is called the capacity of the box or a vessel.
→ The capacity of a rectangular box or a vessel is calculated by multiplying its inner length, width, and height.
→ 1 cubic centimeter = 1 millilitre
→ 1000 cubic centimeter = 1 litre
→ 1 cubic metre =1000 litre
→ 1 cubic metre = 1000000 cubic centimetre
In our everyday life, we often come across objects that occupy spaces – like a water bottle, a box, a tank, or even a cupboard. The amount of space an object takes up is called its volume. Volume helps us understand how much space is inside a three-dimensional object or how much it can hold. In this chapter, we will learn how to measure the volume of different solid shapes, such as cubes, cuboids. We will also explore the formulas used to calculate volume, and understand the units in which volume is measured, like cubic centimetres or liters.
Large and Small & Rectangular Blocks
In the previous classes, we have already learned how to compare the lengths of objects, to find their perimeter. The size of an object can be determined by measuring its length of the objects. Measuring only the length of a rectangular-shaped object is not sufficient to determine its size. Instead, we need to measure both its length and breadth to find its area. To compare the size of two rectangular blocks, we must consider their length, width, and height.
Size of a Rectangular Block & Size as a Number
Look at the rectangular block given below.
The length, width, and height of the rectangular block are 10 cm, 5 cm, and 10 cm, respectively. Also, consider that it is made by stacking smaller blocks, each having length, width, and height as 1 cm, 1 cm, 1 cm.
Let us find out how many small rectangular blocks are contained within the large rectangular block. In the bottom row, there are 10 numbers in length and 5 numbers in width. So the total number of small rectangular blocks is 50.
The height of the larger rectangular block is 10 cm, so we can place 10 smaller blocks along the height. If we stack 50 such columns, each with 10 blocks in height, we get a total of 50 × 10 = 500 blocks. So the size of the larger rectangular block is the same as the size of the small 500 rectangular blocks, each measuring 1 cm in length, 1 cm in width, and 1 cm in height.
We learned that the area of a rectangle with a length of 1 cm and a width of 1 cm is 1 square centimeter. Similarly, the volume of a rectangular block with a length of 1 cm, a width of 1 cm, and a height of 1 cm is 1 cubic centimeter. Therefore, the volume of the above rectangular block is 10 × 5 × 10 = 500 cubic centimeters. That means the volume of a rectangular block can be calculated by multiplying its length, width, and height. If the measurements are in centimeters, then the volume will be in cubic centimeters. If measurements are in metres, then the volume should be in cubic metres.
Question 1.
Find the volume of the given rectangular block.
Answer:
Length of the rectangular block = 20 cm
Width =10 cm
Height = 8 cm
Therefore, Volume = 20 × 10 × 8 = 1600 cubic cm
Question 2.
How many small cubes are used to make this large cube? If one small block is removed from each corner of the large block, how many would be left?
Answer:
The large cube is made by stacking small cubes.
Length = 4 small cubes
Width = 4 small cubes
Height = 4 small cubes
Total number of small cubes = 4 × 4 × 4 = 64
A cube has 8 corners. Removing 1 cube from each corner means a total of 8 cubes are removed.
Therefore the cubes left = 64 – 8 = 56
The number of cubes remaining after removing corners is 56.
Question 3.
All sides of the large cube are painted. How many small cubes would have no paint at all?
Answer:
Total number of small cubes = 3 × 3 × 3 = 27
Only the cubes that are completely inside the large cube will have no paint on them.
The top layer and bottom layer have 9 cubes each, and all have at least one side painted.
In the middle layer, only the outer edge cubes have paint on any of their sides, which means 8 cubes have at least one side painted.
So the total number of cubes with at least one side painted is = 9 + 9 + 8 = 26
Therefore, the small cube with no paint at all = 27 – 26 = 1 cube
Volume Calculation
How do we calculate its volume?
For calculating the volume, we must find out how many cubes of side 1 cm we need to make it.
30 small cubes are needed to make it.
So the volume of the cube is 30 cubic cm.
Or
Volume of the cube = 5 × 3 × 2 = 30 cubic cm.
The volume of a rectangular block is the product of its length, width, and height.
Question 1.
The dimensions of a rectangular block are given below. Find its volume.
(i) Length = 10 cm, Width = 7 cm, Height = 4 cm.
(ii) Length = 5 cm, Width = 5 cm, Height = 5 cm.
(iii) Length = 8 cm, Width = 4 cm, Height = 6 cm.
(iv) Length = 20 cm, Width = 10 cm, Height = 10 cm.
(v) Length = 40 cm, Width = 10 cm, Height = 10 cm.
Answer:
(i) 10 × 7 × 4 = 280 cubic cm
(ii) 5 × 5 × 5 = 125 cubic cm
(iii) 8 × 4 × 6 = 192 cubic cm
(iv) 20 × 10 × 10 = 2000 cubic cm
(v) 40 × 10 × 10 = 4000 cubic cm
Volume and Length
Volume can be calculated when the length, width, and height are given. If any three of these four terms are given, we can find the fourth term.
Question 1.
The volume of a rectangular block is 160 cubic centimetres. Its height and width are 5 centimetres and 4 centimetres respectively. What is its length?
Answer:
Volume = length × breadth × height
160 = length × 5 × 4
160 = length × 20
To find the length, divide 160 by 20
Length = 160 ÷ 20 = 8 cm
Question 2.
A rectangular block of length 23 centimetres and height 6 centimetres has a volume of 1380 cubic centimetres. What is its width?
Answer:
Volume = length × breadth × height
1380 = 23 × width × 6
1380 = width × 138
Width = 1380 ÷ 138 = 10 cm
New Shapes
We can make shapes other than rectangular blocks by stacking cubes.
Question 1.
It is made by stacking cubes of side 1 centimetre. Calculate its volume?
Answer:
1st row (bottom row) = 9 × 9 = 81
2nd row = 7 × 9 = 63
3rd row = 5 × 9 = 45
4th row = 3 × 9 = 27
Total = 81 + 63 + 45 + 27 = 216
Therefore, volume = 216 cubic cm.
Or
If the length and width are 9 in every row, and the height is 4.
Then total number of blocks = 9 × 9 × 4 = 324
Now consider the missing blocks.
1st row (bottom row) = 2 × 9 = 18
2nd row = 4 × 9 = 36
3rd row = 6 × 9 = 54
Total missing blocks = 18 + 36 + 54 = 108
Total number of blocks = 324 – 108 = 216
Therefore, volume = 216 cubic cm.
Question 2.
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. All blocks are of height 1 centimetre. What is the volume of this figure?
Answer:
The blocks are arranged in 5 rows.
Volume of the first square block = 9 × 9 × 1 = 81 cubic cm.
Volume of the second square block = 7 × 7 × 1 = 49 cubic cm.
Volume of the third square block = 5 × 5 × 1 = 25 cubic cm.
Volume of the fourth square block = 3 × 3 × 1 = 9 cubic cm.
Volume of the fifth (top) square block = 1 × 1 × 1 = 1 cubic cm.
Toatal volume of the square blocks = 81 + 49 + 25 + 9 + 1 = 165 cubic cm.
Question 3.
What is the volume of a rectangular block of length 4 centimetres, width 3 centimetres, and height 1 centimetre? If the length, width, and height are doubled, what happens to the volume?
Answer:
Length of the rectangular block = 4 cm
Width = 3 cm
Height = 1 cm
Volume of the rectangular block = 4 × 3 × 1 = 12 cubic cm.
If the length, width, and height are doubled.
Length = 8 cm
Width = 6 cm
Height = 2 cm
Volume = 8 × 6 × 2 = 96 cubic cm.
For a rectangular block,
If the length is doubled, the volume becomes twice.
If the length and width are doubled, the volume becomes four times.
If the length, width, and height are all doubled, the volume becomes eight times.
Large Measures
The volume of a rectangular block is 1 cubic centimetre if its length is 1 centimetre, its width is 1 centimetre, and its height is 1 centimetre.
The volume of a rectangular block is 1 cubic metre if its length is 1 metre, width is h metres, and height is 1 metre.
1 cubic metre = 100 × 100 × 100 = 1000000 cubic centimetre
Then, the volume of a rectangular block, if its length is 5 metres, width 3 metres, and height 2 metres, is 5 × 3 × 2 = 30 cubic metres
If it is converted into cubic centimetres, 30 × 1000000 = 30000000 cubic cm
Question 1.
What is the volume of a platform if its length is 12 metres, width is 8 metres, and height is 75 centimetres?
Answer:
Here, the measurements are both in centimetres and metres.
Convert every value into centimetres.
1200 cm × 800 cm × 75 cm = 72,000,000 cubic cm
If converting it into cubic metres, 72,000,000 ÷ 1000000 = 72 cubic metres
Capacity & Liquid Measures
Capacity refers to the amount a box or a vessel can hold. So it is closely related to volume. That is, the volume is called the capacity of the box or a vessel. The capacity of a rectangular box or a vessel is calculated by multiplying its inner length, width, and height. While considering the thickness of a rectangular box or vessel, the inner and outer dimensions are different.
For this rectangular box, the outer dimensions are greater than the inner dimensions. For calculating the capacity, we have to consider the inner dimensions.
Question 1.
Calculate the capacity when its inner dimensions are of length 20 centimetres, width 10 centimetres, and height 5 centimetres.
Answer:
Capacity = 20 × 10 × 5 = 1000 cubic cm
If we are discussing the quantity of water contained in a rectangular box, it can be expressed in millilitres or litres.
Consider a rectangular box with dimensions of length 1 centimetre, width 1 centimetre, and height 1 centimetre.
Its capacity is calculated as = 1 × 1 × 1 = 1 cubic cm. This is equal to 1 millilitre
If we combine 1000 such boxes, their total capacity becomes 1000 cubic cm, which is equal to 1 litre.
1000 millilitre = 1 litre
Therefore, the capacity of the above-mentioned rectangular box is 1000 cubic cm = 1 litre.
Consider a rectangular box with dimensions of length 10 centimetres, width 10 centimetres, and height 10 centimetres.
Its capacity is calculated as = 10 × 10 × 10 = 1000 cubic cm. This is equal to 1 litre. These relationships can be written like this:
- 1 cubic centimeter = 1 millilitre
- 1000 cubic centimeter = 1 litre
- 1 cubic metre = 1000 litre
- 1 cubic metre = 1000000 cubic centimetre
Question 2.
What is the capacity of a box whose inner length, width, and height are 15 centimetres, 10 centimetres, and 8 centimetres?
Answer:
Capacity = 15 × 10 × 8
= 1200 cubic cm.
= 1000 cubic cm + 200 cubic cm
= 1 litre + 200 millilitre
= 1 litre 200 millilitre
Question 3.
A vessel is filled with water. If a cube of side 1 centimetre is immersed in it, how many cubic centimetres of water would overflow? What if 20 such cubes are immersed?
Answer:
If a cube of side 1 centimetre is immersed in a vessel filled with water, the amount of water that overflows will be equal to the volume (or capacity) of the cube.
Volume of the cube = 1 cm × 1 cm × 1 cm = 1 cubic centimeter
Since 1 cubic centimetre = 1 millilitre
1 millilitre of water will overflow.
If 20 such cubes are immersed.
Each cube displaces 1 millilitre of water.
So, 20 × 1 = 20 millilitres of water will overflow.
Question 4.
A water tank of length 4 metres, width 3 metres, and height 2 metres. How many litres of water does it contain?
Answer:
Capacity of the water tank = 4 × 3 × 2 = 24 cubic metre
Since 1 cubic metre = 1000 litre
24 cubic metre = 24000 litre
Therefore, the tank can hold 24,000 litres of water.
Question 5.
A rectangular tank of length 8 metres and width 6 metres. It contains 96000 litres of water. Calculate the height of the water in the tank?
Answer:
1 cubic metre = 1000 litres
96000 litres = \(\frac {96000}{10000}\) = 96 cubic metres
Volume = length × width × height
96 = 8 × 6 × height
height = 96 ÷ 48 = 2 metre
Question 6.
A swimming pool is 25 metres long, 10 metres wide, and 2 metres deep. It is half-filled. How many litres of water does it contain now?
25 × 10 × 1 = 250 cubic metres = 250000 litres
Suppose the water level is increased by 1 centimetre. How many more litres of water does it contain now?
Answer:
If it is half-filled
Full depth = 2 metre, Half depth = 1 metre
Volume = 25 × 10 × 1 = 250 cubic metres
250 cubic metres = 250 × 1000 = 250,000 litres
If the water level rises by 1 cm
Additional volume = 2500 × 1000 × 1 = 2500000 cubic cm
2500000 cubic cm = \(\frac {2500000}{1000}\) = 2500 litres