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Measures and solids · Ages 13–14

Volume of a prism worksheet

Part of: Prisms & cylinders

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Volume of a prism worksheet

Measures and solids · Ages 13–14

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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. 1.A prism has a base area of 57 cm², and its two ends are 23 cm apart. What is its volume, in cm³?

    Answer:

  2. 2.The prism in the picture has a right-angled triangle as its cross-section, its two shorter sides 3 cm and 12 cm, and it is 5 cm long. What is its volume, in cm³?

    Answer:

  3. 3.The prism in the picture has a trapezium as its cross-section: 8 cm along the top, 16 cm along the bottom, 9 cm high. It is 5 cm long. What is its volume, in cm³?

    Answer:

  4. 4.The prism in the picture has a volume of 252 cm³, and its cross-section is a triangle 8 cm across and 3 cm high. How long is the prism?

    Answer:

  5. 5.The prism in the picture has an L-shaped cross-section, 6 cm wide and 8 cm high, both arms 2 cm thick, and it is 12 cm long. What is its volume, in cm³?

    Answer:

  6. 6.The prism in the picture has a trapezium as its cross-section: 7 cm along the top, 15 cm along the bottom, 4 cm high. It is 17 cm long. What is its volume, in cm³?

    Answer:

  7. 7.The prism in the picture has a volume of 675 cm³, and its cross-section is a triangle 10 cm across and 9 cm high. How long is the prism?

    Answer:

  8. 8.The prism in the picture is 8 cm long with a volume of 320 cm³, its cross-section a trapezium 6 cm along the top and 10 cm along the bottom. How high is the trapezium, in cm?

    Answer:

  9. 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 equal triangles of 26 cm² each. The cross-section is cm²; the prism is 14 cm long, so its volume is cm³.

    Fill in each blank

    Answer:

  10. 10.The prism in the picture is 5 cm long with a volume of 270 cm³, its cross-section a trapezium 3 cm along the top and 15 cm along the bottom. How high is the trapezium, in cm?

    Answer:

Part B: Choose, or true or false (2 marks each)

  1. 11.The prism in the picture has a triangle 12 cm across and 4 cm high as its cross-section, and is 9 cm long. What is its volume?

    • A. 12 × 4 ÷ 2 × 9 = 216 cm³
    • B. 12 × 4 ÷ 2 + 9 = 33 cm³
    • C. (12 + 4) × 9 = 144 cm³
    • D. 12 × 4 × 9 = 432 cm³

    Choose the right answer

    Answer:

  2. 12.A prism 9 cm long whose cross-section is a triangle 7 cm across and 10 cm high has a volume of 630 cm³.

    True or false?

    Answer:

Part C: Word problems (4 marks each)

  1. 13.The picture shows an L-shaped steel bar: its cross-section 7 cm wide and 7 cm high, both arms 2 cm thick, the bar 35 cm long. Each 1 cm³ of steel weighs 7 g. How many grams does the bar weigh?

    Working:

    Answer:

  2. 14.A tent is a triangular prism: the triangle at its front is 190 cm across and 160 cm high, and the tent is 210 cm long. How many m³ of space are inside?

    Working:

    Answer:

  3. 15.A wooden strip with a trapezium cross-section has a volume of 1134 cm³; the trapezium is 5 cm along the top, 13 cm along the bottom and 9 cm high. Find the strip's length: put the steps in order.

    • A. Volume = cross-section × length: 81 × length = 1134
    • B. Length = 1134 ÷ 81 = 14 cm
    • C. Cross-section = (5 + 13) × 9 ÷ 2 = 81

    Write the letters in the right order

    Working:

    Answer:

  4. 16.A model house has a five-sided cross-section: a rectangle 11 cm wide and 9 cm high, with a triangular roof 11 cm across and 2 cm high on top; the house is 19 cm long. The rectangle is cm², the roof cm², and the house's volume cm³.

    Fill in each blank

    Working:

    Answer:

  5. 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 20 bars holds cm³.

    Fill in each blank

    Working:

    Answer:

  6. 18.A swimming pool is 20 m long and 11 m wide, its floor sloping from the shallow end, 2 m deep, to the deep end, 4 m deep. How many m³ of water does the full pool hold?

    Working:

    Answer:

Show the answers and working

Volume of a prism worksheet: Answers and working

Part A: Working out and filling in

  1. 1. 1311 cm³

    A prism's volume = base area × height (the distance between its ends) = 57 × 23 = 1311 cm³.

  2. 2. 90 cm³

    Cross-section 3 × 12 ÷ 2 = 18 cm², volume = cross-section × length = 18 × 5 = 90 cm³.

  3. 3. 540 cm³

    The trapezium: (8 + 16) × 9 ÷ 2 = 108 cm²; volume 108 × 5 = 540 cm³.

  4. 4. 21 cm

    The cross-section is 8 × 3 ÷ 2 = 12 cm², so the length = volume ÷ cross-section = 252 ÷ 12 = 21 cm.

  5. 5. 288 cm³

    Split the L into two rectangles: the bottom arm 6 × 2 = 12 and the upright one 6 × 2 = 12, 24 cm²; volume 24 × 12 = 288 cm³.

  6. 6. 748 cm³

    The trapezium: (7 + 15) × 4 ÷ 2 = 44 cm²; volume 44 × 17 = 748 cm³.

  7. 7. 15 cm

    The cross-section is 10 × 9 ÷ 2 = 45 cm², so the length = volume ÷ cross-section = 675 ÷ 45 = 15 cm.

  8. 8. 5 cm

    The cross-section = 320 ÷ 8 = 40 cm²; (6 + 10) × height ÷ 2 = 40, so the height = 40 × 2 ÷ 16 = 5 cm.

  9. 9. 156, 2184

    Cross-section 6 × 26 = 156 cm², volume 156 × 14 = 2184 cm³.

  10. 10. 6 cm

    The cross-section = 270 ÷ 5 = 54 cm²; (3 + 15) × height ÷ 2 = 54, so the height = 54 × 2 ÷ 18 = 6 cm.

Part B: Choose, or true or false

  1. 11. A. 12 × 4 ÷ 2 × 9 = 216 cm³

    The cross-section is 12 × 4 ÷ 2, times the length 9: 216 cm³.

  2. 12. False

    The cross-section is 7 × 10 ÷ 2, times the length 9: 315 cm³.

Part C: Word problems

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

  1. 13. 5880 g

    The cross-section as two rectangles: 7 × 2 + (7 − 2) × 2 = 24 cm²; volume 24 × 35 = 840 cm³; weight 840 × 7 = 5880 g.

  2. 14. 3.192 m³

    In cm: 190 × 160 ÷ 2 × 210 = 3,192,000 cm³; 1 m³ = 1 000 000 cm³, so 3.192 m³. Changing the lengths to metres first gives the same.

  3. 15. C → A → B

    The cross-section first, 81 cm², then volume ÷ cross-section: 1134 ÷ 81 = 14 cm.

  4. 16. 99, 11, 2090

    11 × 9 = 99; 11 × 2 ÷ 2 = 11; the cross-section is 110 cm², the volume 110 × 19 = 2090 cm³.

  5. 17. 6, 162, 3240

    4 × 3 ÷ 2 = 6; 6 × 27 = 162; 162 × 20 = 3240.

  6. 18. 660 m³

    Seen from the side the pool is a prism with a trapezium cross-section: (2 + 4) × 20 ÷ 2 = 60 m², and its width 11 m is its length: 60 × 11 = 660 m³.

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