A medicine capsule is a cylinder with a hemisphere fixed on each end, all of radius 2.1 mm. Its total volume is 149.688 cubic millimetres. Find the length of the cylindrical part, in millimetres. (Take π = 22/7.)

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Accepted Answer

8. The two hemispheres make one sphere: 4/3\π r^3 = 4/3 × 22/7 × (2.1)^3 = 38.808 mm³. So the cylinder holds 149.688 − 38.808 = 110.88 mm³. Its cross-section is \π r^2 = 22/7(4.41) = 13.86 mm², so length = 110.88 ÷ 13.86 = 8 mm. 10.8 divides the whole volume by the cross-section without removing the ends; 9.4 removes only one hemisphere; 4 halves the correct length.

A medicine capsule is a cylinder with a hemisphere fixed on each end, all of radius 2.1 mm. Its total volume is 149.688 cubic millimetres. Find the length of the cylindrical part, in millimetres. (Take π = 22/7.)

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