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.
Level 1 · Warm-up
1 Two rectangular prisms are joined to make one solid. One has a volume of 90 cm3 and the other 45 cm3. Find the volume of the whole solid. (number of cm3)
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90 + 45 = 135 cm3.
2 A solid is made of a prism 6 cm × 4 cm × 2 cm joined to a prism 3 cm × 4 cm × 2 cm. Find its total volume. (number of cm3)
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6 × 4 × 2 = 48 and 3 × 4 × 2 = 24, so the total is 72 cm3.
3 A block with a volume of 200 cm3 has a piece of volume 35 cm3 removed from it. Find the volume that is left. (number of cm3)
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200 − 35 = 165 cm3.
Level 2 · Core
4 A step-shaped solid splits into a prism 10 cm × 4 cm × 3 cm and a prism 6 cm × 4 cm × 3 cm. Find its total volume. (number of cm3)
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10 × 4 × 3 = 120 and 6 × 4 × 3 = 72, so the solid is 192 cm3.
5 A block 8 cm × 5 cm × 6 cm has a corner piece 3 cm × 5 cm × 2 cm cut away. Find the volume remaining. (number of cm3)
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Block 8 × 5 × 6 = 240 cm3, cut-out 3 × 5 × 2 = 30 cm3, so 210 cm3 is left.
6 A slab 12 cm × 8 cm × 2 cm has a cube of edge 4 cm sitting on top of it. Find the total volume. (number of cm3)
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Slab 12 × 8 × 2 = 192 cm3, cube 4 × 4 × 4 = 64 cm3, total 256 cm3.
Level 3 · Challenge
7 A step-shaped solid is 12 cm wide, 5 cm deep and 8 cm tall overall. A piece 5 cm wide, 5 cm deep and 3 cm tall has been removed from the top corner. Find its volume. (number of cm3)
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Full box 12 × 5 × 8 = 480 cm3, missing piece 5 × 5 × 3 = 75 cm3, so the solid is 405 cm3.
8 A concrete plinth is a slab 100 cm × 60 cm × 10 cm with a block 40 cm × 30 cm × 20 cm standing on top. Find the total volume. (number of cm3)
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Slab 100 × 60 × 10 = 60000 cm3, block 40 × 30 × 20 = 24000 cm3, total 84000 cm3.
9 A box 15 cm × 10 cm × 8 cm has a rectangular notch 5 cm × 10 cm × 3 cm cut out of one edge. Find the volume that is left. (number of cm3)
Show worked solution
Box 15 × 10 × 8 = 1200 cm3, notch 5 × 10 × 3 = 150 cm3, leaving 1050 cm3.