Measures and solids · Ages 12–13
Volume of a prism worksheet
Part of: Prisms
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Volume of a prism worksheet
Measures and solids · Ages 12–13
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.A prism has a base area of 59 cm², and its two ends are 23 cm apart. What is its volume, in cm³?
Answer:
2.The prism in the picture has a right-angled triangle as its cross-section, its two shorter sides 6 cm and 10 cm, and it is 5 cm long. What is its volume, in cm³?
Answer:
3.A prism has a base area of 26 cm², and its two ends are 9 cm apart. What is its volume, in cm³?
Answer:
4.The prism in the picture has an L-shaped cross-section, 6 cm wide and 10 cm high, both arms 2 cm thick, and it is 13 cm long. What is its volume, in cm³?
Answer:
5.The prism in the picture has a trapezium as its cross-section: 3 cm along the top, 9 cm along the bottom, 8 cm high. It is 7 cm long. What is its volume, in cm³?
Answer:
6.The prism in the picture has a volume of 342 cm³, and its cross-section is a triangle 12 cm across and 3 cm high. How long is the prism?
Answer:
7.The prism in the picture has a trapezium as its cross-section: 7 cm along the top, 10 cm along the bottom, 8 cm high. It is 10 cm long. What is its volume, in cm³?
Answer:
8.The prism in the picture is 6 cm long with a volume of 270 cm³, its cross-section a trapezium 3 cm along the top and 12 cm along the bottom. How high is the trapezium, in cm?
Answer:
9.The prism in the picture has a regular hexagon as its cross-section; joined from its centre to its six corners, it splits into 6 identical triangles of 28 cm² each. The cross-section is cm²; the prism is 5 cm long, so its volume is cm³.
Fill in each blank
Answer:
10.The prism in the picture has a regular hexagon as its cross-section; joined from its centre to its six corners, it splits into 6 identical triangles of 22 cm² each. The cross-section is cm²; the prism is 27 cm long, so its volume is cm³.
Fill in each blank
Answer:
Part B: Choose, or true or false (2 marks each)
11.The prism in the picture has a triangle 10 cm across and 7 cm high as its cross-section, and is 13 cm long. What is its volume?
- A. 10 × 7 ÷ 2 + 13 = 48 cm³
- B. 10 × 7 × 13 = 910 cm³
- C. (10 + 7) × 13 = 221 cm³
- D. 10 × 7 ÷ 2 × 13 = 455 cm³
Choose the right answer
Answer:
12.A prism 8 cm long whose cross-section is a triangle 12 cm across and 6 cm high has a volume of 576 cm³.
True or false?
Answer:
Part C: Word problems (4 marks each)
13.A wooden strip with a trapezium cross-section has a volume of 480 cm³; the trapezium is 4 cm along the top, 8 cm along the bottom and 5 cm high. Find the strip's length: put the steps in order.
- A. Length = 480 ÷ 30 = 16 cm
- B. Volume = cross-section × length: 30 × length = 480
- C. Cross-section = (4 + 8) × 5 ÷ 2 = 30
Write the letters in the right order
Working:
Answer:
14.A swimming pool is 37 m long and 22 m wide, its floor sloping from the shallow end, 1 m deep, to the deep end, 3 m deep. How many m³ of water does the full pool hold?
Working:
Answer:
15.A tent is a triangular prism: the triangle at its front is 160 cm across and 170 cm high, and the tent is 270 cm long. How many m³ of space are inside?
Working:
Answer:
16.The picture shows an L-shaped steel bar: its cross-section 8 cm wide and 8 cm high, both arms 3 cm thick, the bar 12 cm long. Each 1 cm³ of steel weighs 8 g. How many grams does the bar weigh?
Working:
Answer:
17.A triangular chocolate bar is 27 cm long, its cross-section a triangle 4 cm across and 3 cm high. The cross-section is cm², one bar's volume cm³; a box of 10 bars holds cm³.
Fill in each blank
Working:
Answer:
18.A model house has a five-sided cross-section: a rectangle 4 cm wide and 5 cm high, with a triangular roof 4 cm across and 4 cm high on top; the house is 11 cm long. The rectangle is cm², the roof cm², and the house's volume cm³.
Fill in each blank
Working:
Answer:
Show the answers and working
Volume of a prism worksheet: Answers and working
Part A: Working out and filling in
1. 1357 cm³
A prism's volume = base area × height (the distance between its ends) = 59 × 23 = 1357 cm³.
2. 150 cm³
Cross-section 6 × 10 ÷ 2 = 30 cm², volume = cross-section × length = 30 × 5 = 150 cm³.
3. 234 cm³
A prism's volume = base area × height (the distance between its ends) = 26 × 9 = 234 cm³.
4. 364 cm³
Split the L into two rectangles: the bottom arm 6 × 2 = 12 and the upright one 8 × 2 = 16, 28 cm²; volume 28 × 13 = 364 cm³.
5. 336 cm³
The trapezium: (3 + 9) × 8 ÷ 2 = 48 cm²; volume 48 × 7 = 336 cm³.
6. 19 cm
The cross-section is 12 × 3 ÷ 2 = 18 cm², so the length = volume ÷ cross-section = 342 ÷ 18 = 19 cm.
7. 680 cm³
The trapezium: (7 + 10) × 8 ÷ 2 = 68 cm²; volume 68 × 10 = 680 cm³.
8. 6 cm
The cross-section = 270 ÷ 6 = 45 cm²; (3 + 12) × height ÷ 2 = 45, so the height = 45 × 2 ÷ 15 = 6 cm.
9. 168, 840
Cross-section 6 × 28 = 168 cm², volume 168 × 5 = 840 cm³.
10. 132, 3564
Cross-section 6 × 22 = 132 cm², volume 132 × 27 = 3564 cm³.
Part B: Choose, or true or false
11. D. 10 × 7 ÷ 2 × 13 = 455 cm³
The cross-section is 10 × 7 ÷ 2, times the length 13: 455 cm³.
12. False
The cross-section is 12 × 6 ÷ 2, times the length 8: 288 cm³.
Part C: Word problems
Marking: 2 for the working, 1 for the answer, 1 for the sentence.
13. C → B → A
The cross-section first, 30 cm², then volume ÷ cross-section: 480 ÷ 30 = 16 cm.
14. 1628 m³
Seen from the side the pool is a prism with a trapezium cross-section: (1 + 3) × 37 ÷ 2 = 74 m², and its width 22 m is its length: 74 × 22 = 1628 m³.
15. 3.672 m³
In cm: 160 × 170 ÷ 2 × 270 = 3,672,000 cm³; 1 m³ = 1 000 000 cm³, so 3.672 m³. Changing the lengths to metres first gives the same.
16. 3744 g
The cross-section as two rectangles: 8 × 3 + (8 − 3) × 3 = 39 cm²; volume 39 × 12 = 468 cm³; weight 468 × 8 = 3744 g.
17. 6, 162, 1620
4 × 3 ÷ 2 = 6; 6 × 27 = 162; 162 × 10 = 1620.
18. 20, 8, 308
4 × 5 = 20; 4 × 4 ÷ 2 = 8; the cross-section is 28 cm², the volume 28 × 11 = 308 cm³.
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