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.
15 questions · official format, shuffled order
1 What is the surface area of a closed box 9 cm long, 4 cm wide and 3 cm high?
Show worked solution
2(36 + 27 + 12) = 2 × 75 = 150 cm2. (75 counts each pair once; 108 is the volume.)
2 A triangular prism is 10 cm long. Its ends are right-angled triangles with shorter sides 5 cm and 12 cm. What is its surface area?
Show worked solution
The slant side is 13. Ends 2 × 30 = 60; rectangles (5 + 12 + 13) × 10 = 300. Total 360 cm2. (300 forgets the two ends.)
3 A cube has a volume of 343 cm3. What is its surface area?
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Edge 7 cm, so 6 × 49 = 294 cm2. (196 uses only four faces.)
4 A closed cylinder has radius 3 cm and height 8 cm. What is its total surface area?
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2π × 9 + 2π × 3 × 8 = 18π + 48π = 66π cm2. (48π is the curved surface alone; 57π includes only one circle.)
5 A cylindrical bucket with no lid has radius 6 cm and height 5 cm. What is its outside surface area?
Show worked solution
π × 36 + 2π × 6 × 5 = 36π + 60π = 96π cm2. (132π includes a lid that is not there.)
6 What is the volume of a cylinder with diameter 10 cm and height 6 cm?
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π × 52 × 6 = 150π cm3. (600π uses the diameter as the radius.)
7 A cylinder has volume 28π cm3 and radius 2 cm. What is its height?
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4h = 28, so h = 7 cm. (14 divides by the radius instead of the radius squared.)
8 A prism has a cross-section of area 21 cm2 and a volume of 189 cm3. How long is it?
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189 ÷ 21 = 9 cm. (210 adds instead of dividing; 168 subtracts.)
9 A rectangular container has a base 24 cm by 10 cm. To what height will 3.6 L of water fill it?
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3600 ÷ 240 = 15 cm. (1.5 cm treats 1 L as 100 cm3.)
10 A solid block 10 cm by 6 cm by 4 cm has a 2 cm cube cut out of one corner. What volume is left?
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240 − 8 = 232 cm3. (236 subtracts 2 × 2 = 4 instead of 23.)
11 A cylindrical jug has radius 10 cm and height 20 cm. Using π ≈ 3, how many 250 mL cups can it fill?
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3 × 100 × 20 = 6000 mL, and 6000 ÷ 250 = 24 cups. (240 divides by 25 instead of 250.)
12 Two cubes with 3 cm edges are glued together face to face. What is the surface area of the new solid?
Show worked solution
2 × 54 − 2 × 9 = 90 cm2. (99 hides only one face; 108 hides none.)
13 A closed cylinder has radius 3 cm and height 4 cm.
1 Its curved surface area is 24π cm2.
2 Its volume is 36π cm3.
3 Its total surface area is 33π cm2.
Which statements are correct?
1 Its curved surface area is 24π cm2.
2 Its volume is 36π cm3.
3 Its total surface area is 33π cm2.
Which statements are correct?
Show worked solution
2π × 3 × 4 = 24π (1 ✓). π × 9 × 4 = 36π (2 ✓). 24π + 2 × 9π = 42π; 33π adds only one circle (3 ✗). 1 and 2.
14 The radius of a cylinder is doubled and its height is kept the same. What happens to its volume?
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(2r)2 = 4r2, so the volume is × 4. (× 8 would need every length doubled.)
15 A rectangular prism measures 6 cm by 4 cm by 2 cm.
1 Its volume is 48 cm3.
2 Its surface area is 88 cm2.
3 A cube with the same volume would have 4 cm edges.
Which statements are correct?
1 Its volume is 48 cm3.
2 Its surface area is 88 cm2.
3 A cube with the same volume would have 4 cm edges.
Which statements are correct?
Show worked solution
6 × 4 × 2 = 48 (1 ✓). 2(24 + 12 + 8) = 88 (2 ✓). A 4 cm cube has volume 64, not 48 (3 ✗). 1 and 2.