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 A cylinder with radius 2 cm and height 5 cm stands on top of a 4 cm cube. Find the volume of the solid.
Show worked solution
Cube: 43 = 64. Cylinder: π × 22 × 5 = 20π. Total 64 + 20π cm3. 64 + 10π forgets to square the radius; 64 + 40π uses 2πrh, an area; 64 + 80π uses the diameter 4 as the radius.
2 This step block is a 6 cm × 2 cm rectangle with a 2 cm × 3 cm rectangle standing on its left end, and it is 5 cm deep. Find the area of its front face and its volume.
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Front: 6 × 2 + 2 × 3 = 12 + 6 = 18 cm2. Volume: 18 × 5 = 90 cm3.
3 A full 3 L jug is poured into cups that each hold 200 mL. How many cups can be filled?
Show worked solution
3 L = 3000 mL, and 3000 ÷ 200 = 15 cups.
Level 2 · Core
4 A block 8 cm long, 5 cm wide and 4 cm high has a hole of radius 1 cm drilled right through it along its 8 cm length. Find the volume left.
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Block: 8 × 5 × 4 = 160. Hole: π × 12 × 8 = 8π. Left: 160 − 8π cm3. 160 − π leaves out the hole's length; 160 − 16π uses 2πrh; 160 − 32π uses the diameter 2 as the radius.
5 A pipe is 5 cm long, with outer radius 6 cm and a hole of radius 4 cm.Find the volume of the outer cylinder, of the hole, and of the material.
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Outer: π × 36 × 5 = 180π. Hole: π × 16 × 5 = 80π. Material: 180π − 80π = 100π cm3.
6 A fish tank 40 cm long, 25 cm wide and 30 cm high is filled using a 2.5 L bucket. How many full buckets are needed?
Show worked solution
40 × 25 × 30 = 30 000 cm3 = 30 L, and 30 ÷ 2.5 = 12 buckets.
Level 3 · Challenge
7 Three statements:
1 A solid cylinder with r = 3 cm and h = 4 cm, with a hole of radius 1 cm drilled along its axis, has a volume of 32π cm3.
2 Cutting a 2 cm cube from each of the eight corners of a 10 cm cube leaves 936 cm3.
3 Using π ≈ 3, a full 3 L jug fills 12 cylindrical glasses with r = 3 cm and h = 10 cm.
Which statements are correct?
1 A solid cylinder with r = 3 cm and h = 4 cm, with a hole of radius 1 cm drilled along its axis, has a volume of 32π cm3.
2 Cutting a 2 cm cube from each of the eight corners of a 10 cm cube leaves 936 cm3.
3 Using π ≈ 3, a full 3 L jug fills 12 cylindrical glasses with r = 3 cm and h = 10 cm.
Which statements are correct?
Show worked solution
π × 9 × 4 − π × 1 × 4 = 36π − 4π = 32π (1 ✓). 1000 − 8 × 8 = 936 (2 ✓). One glass is π × 9 × 10 = 90π ≈ 270 cm3, and 3000 ÷ 270 ≈ 11.1, so the jug fills only 11 full glasses (3 ✗). 1 and 2.
8 Cylinder A (radius 6 cm, height 10 cm) is full of water. All of it is poured into the empty, taller cylinder B, which has radius 3 cm.Find the volume of the water, and how deep it is in B.
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Water: π × 36 × 10 = 360π cm3. In B: 9π × depth = 360π, so the depth is 360 ÷ 9 = 40 cm. (B's radius squared is a quarter of A's, so the water is four times as deep.)
9 This prism is 7 cm long. Its cross-section is a 10 cm × 6 cm rectangle with a 4 cm wide, 3 cm deep notch cut from the middle of its top edge. Find its volume, in cm3.
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A = 10 × 6 − 4 × 3 = 60 − 12 = 48 cm2, so V = 48 × 7 = 336.