This set has 11 original questions, ordered from easier to harder. They cover prisms, cylinders and cones, unit conversion, missing lengths and estimating, the five skills in volume and capacity.
Use a calculator unless a question says otherwise. Try each question with the answer closed, write the unit on every line, then open the worked answer and compare your method. Unless stated, give non-exact answers to 3 significant figures.
Questions
1. A cuboid measures 12 cm by 5 cm by 4 cm. Find its volume.
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Volume = 12 × 5 × 4 = 60 × 4 = 240 cm³.
2. A triangular prism has a triangular end with base 9 cm and perpendicular height 4 cm. The prism is 12 cm long. Find its volume.
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Area = ½ × 9 × 4 = 18 cm². Volume = 18 × 12 = 216 cm³.
3. (a) Write 4.2 litres in cm³. (b) Write 0.36 m³ in litres.
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(a) 4.2 × 1000 = 4200 cm³.
(b) 1 m³ = 1000 litres, so 0.36 × 1000 = 360 litres.
4. A cylinder has radius 5 cm and height 12 cm. Find its volume.
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V = π × 5² × 12 = π × 25 × 12 = 300π = 942.47… so 942 cm³.
5. A prism has a trapezium as its end face. The parallel sides are 5 cm and 9 cm, and the perpendicular distance between them is 6 cm. The prism is 20 cm long. (a) Find its volume. (b) Give the capacity in millilitres.
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(a) Area = ½ × (5 + 9) × 6 = ½ × 14 × 6 = 42 cm². Volume = 42 × 20 = 840 cm³.
(b) 1 cm³ = 1 mL, so the capacity is 840 mL.
6. A cone has base radius 9 cm and vertical height 10 cm. Find its volume.
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V = ⅓ × π × 9² × 10 = ⅓ × π × 81 × 10 = 270π = 848.23… so 848 cm³.
7. A cylindrical tank has radius 0.5 m and height 1.2 m. (a) Find its capacity in litres. (b) It is filled at 20 litres per minute. How long does it take to fill, in minutes?
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(a) V = π × 0.5² × 1.2 = π × 0.25 × 1.2 = 0.3π = 0.9424… m³. Multiply by 1000: 942 litres.
(b) Time = 942.47… ÷ 20 = 47.12… so 47.1 minutes.
8. A cylinder has volume 1500 cm³ and radius 7 cm. Find its height.
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h = V ÷ (πr²) = 1500 ÷ (π × 49) = 1500 ÷ 153.93… = 9.744… so 9.74 cm.
9. A solid is made from a cylinder with radius 3 cm and height 8 cm, with a cone of radius 3 cm and vertical height 4 cm fixed on top. Find the total volume.
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Cylinder: π × 3² × 8 = 72π. Cone: ⅓ × π × 3² × 4 = 12π. Total = 84π = 263.89… so 264 cm³.
10. A cone has volume 200 cm³ and vertical height 6 cm. Find its base radius.
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V = ⅓πr²h, so r² = 3V ÷ (πh) = 600 ÷ (6π) = 100 ÷ π = 31.83… Then r = √31.83… = 5.641… so 5.64 cm.
11. A student finds the volume of a cylinder with radius 2.9 cm and height 9.1 cm and writes 2404 cm³. Estimate the volume, say whether 2404 is plausible, and find the correct answer.
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Estimate: π ≈ 3, r ≈ 3, h ≈ 9, so 3 × 9 × 9 = 243 cm³. The answer 2404 is ten times too big, so it is not plausible. Correct value: π × 2.9² × 9.1 = π × 8.41 × 9.1 = π × 76.531 = 240.4… so 240 cm³.
If you got these wrong
| What went wrong | Likely questions | Go to |
|---|---|---|
| Used a slanting side, or forgot the end-face area | 2, 5 | Prism volume from a cross-section |
| Wrong radius, missed the one third, or used a slant height | 4, 6, 9 | Cylinder and cone |
| Answer out by 10, 100 or 1000 | 3, 7 | Volume units and capacity |
| Could not rearrange, or forgot the square root | 8, 10 | Reverse-dimension problems |
| Did not notice an answer was the wrong size | 11 | Plausibility estimates |
For the arithmetic inside these questions, the non-calculator working trainer gives extra exact-value practice. When you find a repeat pattern, record it in the mistake log and retest queue and try a new question of the same type a few days later.
Some students complete a set like this and still feel unsure why certain answers were marked wrong. Online one-to-one Mathematics tuition gives you a teacher who can trace each error back to its cause while you talk it through.