Perimeter, area and volume · Ages 10–11

Combined solids, and a side from a volume worksheet

Part of: Volume

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Perimeter, area and volume · Ages 10–11

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Write each answer in the space. For word problems, show your working and write a sentence answer.

1.A cuboid's volume is 700 cm³; it is 10 cm long and 10 cm wide. How many centimetres high is it?
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2.A cube's volume is 1000 cm³. How many centimetres long is each side?
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3.A cube's volume is 64 cm³. How many centimetres long is each side?
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4.A cuboid's volume is 196 cm³; it is 14 cm long and 2 cm wide. How many centimetres high is it?
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5.A solid is two cuboids, one on the other: the bottom is 14 cm by 7 cm by 6 cm, the top 4 cm by 7 cm by 2 cm. What is the solid's volume in cm³?
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6.A cuboid's base area is 29 cm² and its height 11 cm. What is its volume in cm³?
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7.A cuboid's base area is 56 cm² and its height 4 cm. What is its volume in cm³?
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8.A solid is two cuboids, one on the other: the bottom is 14 cm by 4 cm by 5 cm, the top 4 cm by 4 cm by 5 cm. What is the solid's volume in cm³?
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9.A wooden block 17 cm by 8 cm by 8 cm has a cuboid 2 cm by 3 cm by 3 cm cut out of it. What volume is left, in cm³?
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10.A wooden block 16 cm by 7 cm by 5 cm has a cuboid 4 cm by 4 cm by 2 cm cut out of it. What volume is left, in cm³?
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13.A cuboid fish tank is 50 cm long and 20 cm wide. 8,000 cm³ of water is poured in. How deep is the water, in cm?
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14.A concrete flight has 3 steps, each 18 cm high and 28 cm deep, and the flight is 90 cm wide. From the side, front to back, it is 1, 2 and 3 steps tall (every step built down to the ground). What is its volume in cm³?
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15.Cuboid A is 9 cm by 8 cm by 5 cm. Cuboid B has a base 2 cm by 12 cm and the same volume as A. How many centimetres high is B?
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16.A wooden block 20 cm by 24 cm by 8 cm is sawn into cubes with 4 cm sides. At most how many cubes is that?
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17.Cuboid A is 4 cm by 8 cm by 12 cm. Cuboid B has a base 6 cm by 8 cm and the same volume as A. How many centimetres high is B?
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18.A cuboid fish tank is 20 cm long and 20 cm wide. 3,200 cm³ of water is poured in. How deep is the water, in cm?
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Show the answers and working

Combined solids, and a side from a volume worksheet: Answers and working

1. 7 cm
Volume = length × width × height. Work out the base area, 10 × 10, first.
Height = volume ÷ (length × width) = 700 ÷ 100 = 7.
2. 10 cm
A cube's length, width and height are equal. Which number times itself three times makes 1000?
Find the number multiplied by itself three times to make 1000: 10 × 10 × 10 = 1000.
3. 4 cm
A cube's length, width and height are equal. Which number times itself three times makes 64?
Find the number multiplied by itself three times to make 64: 4 × 4 × 4 = 64.
4. 7 cm
Volume = length × width × height. Work out the base area, 14 × 2, first.
Height = volume ÷ (length × width) = 196 ÷ 28 = 7.
5. 644 cm³
Split the solid into the bottom and top cuboids and find each volume.
Work each out and add: 588 + 56 = 644.
6. 319 cm³
A cuboid's volume = base area × height, and the base area is given.
Volume = base area × height = 29 × 11 = 319.
7. 224 cm³
A cuboid's volume = base area × height, and the base area is given.
Volume = base area × height = 56 × 4 = 224.
8. 360 cm³
Split the solid into the bottom and top cuboids and find each volume.
Work each out and add: 280 + 80 = 360.
9. 1070 cm³
Find the whole block's volume first, then think what to do with the part cut out.
The big block less the part cut out: 1088 − 18 = 1070.
10. 528 cm³
Find the whole block's volume first, then think what to do with the part cut out.
The big block less the part cut out: 560 − 32 = 528.

11. D. 96 ÷ (12 × 2)
Length × width × height = 96, and the base area is length × width. How do you get the height from the volume and the base area?
Height = volume ÷ base area = 96 ÷ (12 × 2) = 4.
12. A. 48 ÷ (4 × 4)
Length × width × height = 48, and the base area is length × width. How do you get the height from the volume and the base area?
Height = volume ÷ base area = 48 ÷ (4 × 4) = 3.

Marking: 2 for the working, 1 for the answer, 1 for the sentence.

13. 8 cm
The water is a cuboid too: its volume = base area × depth. Work out the base area, 50 × 20, first.
Depth = water's volume ÷ base area = 8,000 ÷ (50 × 20) = 8.
14. 272160 cm³
From the side, how many equal blocks does the flight split into? Each is 90 wide, 28 deep and 18 high.
Split it into 1 + 2 + 3 = 6 equal blocks of 90 × 28 × 18 = 45360: 6 × 45360 = 272160.
15. 15 cm
The volumes are equal. Find A's volume, 9 × 8 × 5, first.
A's volume is 360; B's height = 360 ÷ (2 × 12) = 15.
16. 60 cubes
Take each direction in turn: how many 4 cm lengths fit in 20 cm? Then the width and height.
Along each edge: 20 ÷ 4, 24 ÷ 4, 8 ÷ 4; 5 × 6 × 2 = 60.
17. 8 cm
The volumes are equal. Find A's volume, 4 × 8 × 12, first.
A's volume is 384; B's height = 384 ÷ (6 × 8) = 8.
18. 8 cm
The water is a cuboid too: its volume = base area × depth. Work out the base area, 20 × 20, first.
Depth = water's volume ÷ base area = 3,200 ÷ (20 × 20) = 8.

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