A hemispherical depression of radius 2.8 cm is scooped out of one face of a solid wooden cube of edge 9 cm. Find the volume of wood left, in cubic centimetres, correct to two decimals. (Take π = 22/7.)

Question

Accepted Answer

683.01. Cube = 9³ = 729 cm³. Hemisphere removed = 2/3\π r^3 = 2/3 × 22/7 × (2.8)^3 = 2/3(68.99) = 45.99 cm³. Wood left = 729 − 45.99 = 683.01 cm³. 774.99 adds the depression instead of subtracting it; 637.01 uses 4/3\π r^3 (a whole sphere) for a depression that is only half a sphere; 729 forgets the scoop.

A hemispherical depression of radius 2.8 cm is scooped out of one face of a solid wooden cube of edge 9 cm. Find the volume of wood left, in cubic centimetres, correct to two decimals. (Take π = 22/7.)

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