Perimeter, area and volume · Ages 10–11
Volume worksheet
Covers: Volume by counting cubes, Units of volume, Volume of cubes and cuboids, Combined solids, and a side from a volume, Square roots and cube roots
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Volume worksheet
Perimeter, area and volume · Ages 10–11
Numsprite
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Name:Date:Score:／48
Write each answer in the space. For word problems, show your working and write a sentence answer.
Part A: Working out and filling in (2 marks each)
1.The cuboid is built of 1 cm³ cubes. What is its volume in cm³?
Answer:
2.The solid is built of 1 cm³ cubes (every column stands on the ground). What is its volume in cm³?
Answer:
3.2 m³ = cm³
Answer:
4.Volume of the solid = ? cm³
Answer:
5.Volume of the cube = ? cm³
Answer:
6.A cuboid's base area is 44 cm² and its height 8 cm. What is its volume in cm³?
Answer:
7.A solid is two cuboids, one on the other: the bottom is 15 cm by 5 cm by 5 cm, the top 6 cm by 5 cm by 6 cm. What is the solid's volume in cm³?
Answer:
8.A square has an area of 121 cm². How many centimetres long is each side?
Answer:
9.60 lies between two whole numbers next to each other. What is the smaller one?
Answer:
Part B: Choose, or true or false (2 marks each)
10.These four solids are built of 1 cm³ cubes. Which has the largest volume?
- A
- B
- C
- D
Choose the right picture
Answer:
11.A grain of rice has a volume of about 28 ___. Which unit goes in the blank?
- A. cubic kilometres (km³)
- B. cubic millimetres (mm³)
- C. square millimetres (mm²)
- D. cubic centimetres (cm³)
Choose the right answer
Answer:
12.7 m³ = 7,000,000 cm³
True or false?
Answer:
Part C: Word problems (4 marks each)
13.Ming builds the solid in the picture from 1 cm³ blocks (every column stands on the ground), then adds 8 more. What is the volume now, in cm³?
Working:
Answer:
14.The solid is built of 1 cm³ cubes (every column stands on the ground). At least how many more cubes make it a cuboid 3 cubes long, 2 wide and 3 high?
Working:
Answer:
15.A room is 4 m long, 4 m wide and 4 m high. What is its volume in m³?
Working:
Answer:
16.A cube-shaped ornament has edges 4 cm long. What is its volume, in cubic centimetres?
Working:
Answer:
17.A concrete flight has 3 steps, each 19 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?
Working:
Answer:
18.Ka-lok uses 216 cubes of 1 cm³ to build exactly one solid big cube. What is the area of one face of the big cube, in cm²?
Working:
Answer:
Show the answers and working
Volume worksheet: Answers and working
Part A: Working out and filling in
1. 6 cm³
Count the cubes in one layer first, then count the layers.
3 × 2 = 6 a layer, 1 layers: 6 × 1 = 6.
2. 6 cm³
Go column by column: count each back column, then each front one.
Column by column: back 2 + 1 + 1, front 2 + 0 + 0: 6 cubes.
3. 2000000
1 m = 100 cm, so 1 m³ = 100 × 100 × 100 cm³. Work that out first.
1 m³ = 1,000,000 cm³, so 2 m³ = 2,000,000 cm³.
4. Volume of the solid = 8 cm³
One layer is 2 × 1 = 2 small cubes, and there are 4 layers: 2 × 4 = 8 (count the hidden ones too), so 8 cm³
5. Volume of the cube = 125 cm³
A cube's volume is edge × edge × edge: 5 × 5 = 25, 25 × 5 = 125, so 125 cm³
6. 352 cm³
A cuboid's volume = base area × height, and the base area is given.
Volume = base area × height = 44 × 8 = 352.
7. 555 cm³
Split the solid into the bottom and top cuboids and find each volume.
Work each out and add: 375 + 180 = 555.
8. 11 cm
Area = side × side. Which number times itself makes 121?
Area = side × side, so the side is 121 = 11: 11 × 11 = 121.
9. 7
Find the two square numbers either side of 60: one just below it and one just above.
7 × 7 = 49 and 8 × 8 = 64; 49 < 60 < 64, so 60 is between 7 and 8.
Part B: Choose, or true or false
10. A
For each one, work out the cubes in a layer times the layers, then compare the four.
Count each one's cubes (a layer × layers); the most cubes is the largest volume.
11. B. cubic millimetres (mm³)
Compare a grain of rice with a 1 cm cube: which is bigger? Then choose the unit.
A grain of rice is tiny, so its volume is in cubic millimetres: 1 cm³ is already 1000 mm³.
12. True
1 m³ = 100 × 100 × 100 cm³. Work that out, multiply by 7, then compare with 7,000,000.
1 m = 100 cm, so 1 m³ = 100 × 100 × 100 = 1,000,000 cm³, and 7 m³ = 7 × 1,000,000 = 7,000,000 cm³.
Part C: Word problems
Marking: 2 for the working, 1 for the answer, 1 for the sentence.
13. 18 cm³
Count the picture's blocks column by column first, then add the 8.
The picture has 10 blocks; with 8 more: 18 cm³.
14. 7 cubes
Work out how many cubes a 3 × 2 × 3 cuboid needs, then count how many the picture has.
The cuboid needs 3 × 2 × 3 = 18; there are 11: 7 more.
15. 64 m³
Volume = length × width × height. All three are in metres, so the answer is in cubic metres.
4 × 4 × 4 = 64 m³: a room is big enough for cubic metres.
16. A cube-shaped ornament has edges 4 cm long. What is its volume, in cubic centimetres? (Answer: 64 cm³)
4 × 4 × 4 = 64
17. 287280 cm³
From the side, how many equal blocks does the flight split into? Each is 90 wide, 28 deep and 19 high.
Split it into 1 + 2 + 3 = 6 equal blocks of 90 × 28 × 19 = 47880: 6 × 47880 = 287280.
18. 36 cm²
Find the big cube's edge first: which number times itself three times makes 216?
Edge = 3216 = 6 cm, so a face is 6 × 6 = 36 cm².
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