A solid toy is a cone of radius 3 cm and height 14 cm mounted on a hemisphere of radius 3 cm. The toy is melted and recast as a solid cylinder of radius 2 cm. Find the height of the cylinder, in centimetres.

Question

Accepted Answer

15. Cone = 1/3\π (9)(14) = 42\π cm³ and hemisphere = 2/3\π (27) = 18\π cm³, so the toy = 60π cm³. Recast: \π (2)^2 h = 4\π h = 60\π , so h = 15 cm; π cancels throughout. 10.5 uses the cone only; 4.5 uses the hemisphere only; 6.67 keeps the toy's radius 3 cm for the new cylinder instead of 2 cm.

A solid toy is a cone of radius 3 cm and height 14 cm mounted on a hemisphere of radius 3 cm. The toy is melted and recast as a solid cylinder of radius 2 cm. Find the height of the cylinder, in centimetres.

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