A solid cylinder of radius 4.2 cm and height 12 cm has a hemisphere of the same radius scooped out of its top face and a cone of the same radius and depth 5 cm scooped out of its bottom face. Find the volume of the solid that remains, in cubic centimetres, correct to two decimals. (Take π = 22/7.)

Question

Accepted Answer

417.65. Base area \π r^2 = 22/7(17.64) = 55.44 cm², so the cylinder = 55.44 × 12 = 665.28 cm³. Hemisphere removed = 2/3\π r^3 = 2/3 × 22/7 × 74.088 = 155.23 cm³. Cone removed = 1/3(55.44)(5) = 92.40 cm³. Remaining = 665.28 − 155.23 − 92.40 = 417.65 cm³. 912.91 adds both cavities instead of subtracting them; 510.05 removes only the hemisphere; 572.88 removes only the cone.

A solid cylinder of radius 4.2 cm and height 12 cm has a hemisphere of the same radius scooped out of its top face and a cone of the same radius and depth 5 cm scooped out of its bottom face. Find the volume of the solid that remains, in cubic centimetres, correct to two decimals. (Take π = 22/7.)

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