Work through the levels in order. Type your answer and press Check — open the worked solution if you get stuck. Answers like -6, 3/4 or 0.25 are typed exactly as shown. A ⭐ Bonus Challenge at the end is extra credit — skip it if the rest was hard work.
Level 1 · Warm-up
1 The cross-section of this prism is a triangle with base 8 cm and perpendicular height 5 cm. The prism is 6 cm long. Find its volume.
Show worked solution
A = ½ × 8 × 5 = 20 cm2, so V = 20 × 6 = 120 cm3. 240 cm3 forgets the ½; 20 cm3 is the area of the triangle, never multiplied by the length; 40 cm3 is 8 × 5 with neither.
2 A box is 25 cm long, 20 cm wide and 12 cm high. Find its volume, and how many litres it holds.
Show worked solution
V = 25 × 20 × 12 = 6000 cm3 = 6000 mL = 6 L.
3 This box has a square base with 4 cm sides and a volume of 112 cm3. Find its height in cm.
Show worked solution
Base area 4 × 4 = 16 cm2, so h = 112 ÷ 16 = 7. Check: 16 × 7 = 112 ✓.
Level 2 · Core
4 A cylinder has a diameter of 14 cm and a height of 2 cm. Find its volume.
Show worked solution
r = 7, so V = π × 49 × 2 = 98π cm3. 392π cm3 uses 14 as the radius; 49π cm3 is only the area of the circle, never multiplied by the height; 28π cm3 is 2πrh, the curved surface area.
5 A cylindrical jug has radius 10 cm and height 25 cm. Find its volume in terms of π. Then, using π ≈ 3, find roughly how many litres it holds.
Show worked solution
V = π × 100 × 25 = 2500π cm3. With π ≈ 3: 7500 cm3 = 7500 mL = 7.5 L.
6 A cylinder has radius 6 cm and volume 252π cm3. Find its height in cm.
Show worked solution
π × 36 × h = 252π, so h = 252 ÷ 36 = 7.
Level 3 · Challenge
7 Three statements:
1 A 2 L carton holds 2000 cm3.
2 Using π ≈ 3, a cylinder with r = 4 cm and h = 5 cm holds more than a cube with 8 cm edges.
3 A prism 10 cm long whose cross-section is a trapezium with parallel sides 4 cm and 8 cm, 5 cm apart, has a volume of 300 cm3.
Which statements are correct?
1 A 2 L carton holds 2000 cm3.
2 Using π ≈ 3, a cylinder with r = 4 cm and h = 5 cm holds more than a cube with 8 cm edges.
3 A prism 10 cm long whose cross-section is a trapezium with parallel sides 4 cm and 8 cm, 5 cm apart, has a volume of 300 cm3.
Which statements are correct?
Show worked solution
2 L = 2000 mL = 2000 cm3 (1 ✓). The cylinder is 16π × 5 = 80π ≈ 240 cm3, far less than the cube's 512 cm3 (2 ✗). A = ½ × (4 + 8) × 5 = 30, and 30 × 10 = 300 (3 ✓). 1 and 3.
8 A rectangular tank has a base 50 cm by 40 cm. It holds 30 L of water. How deep is the water? How many more litres would raise the water to a depth of 45 cm?
Show worked solution
30 L = 30 000 cm3, and 30 000 ÷ 2000 = 15 cm. To reach 45 cm the water must rise 30 cm: 2000 × 30 = 60 000 cm3 = 60 L.
9 This cylinder is 5 cm tall and has a volume of 320π cm3. Find its radius in cm.
Show worked solution
5πr2 = 320π, so r2 = 64 and r = 8.