A solid made of a cylinder of radius 6 cm and height 13 cm with a hemisphere of the same radius fixed on one end is melted down and recast into small solid cones, each of radius 3 cm and height 4 cm. How many cones are obtained?

Question

Accepted Answer

51. Volume is conserved when a solid is melted, and π cancels throughout. Cylinder = \π (36)(13) = 468\π cm³; hemisphere = 2/3\π (216) = 144\π cm³, so the solid = 612π cm³. One cone = 1/3\π (9)(4) = 12\π cm³. Number = 612 ÷ 12 = 51. 39 melts down the cylinder only and forgets the hemisphere; 17 drops the 1/3 from the cone; 69 uses 4/3\π r^3 for the hemisphere.

A solid made of a cylinder of radius 6 cm and height 13 cm with a hemisphere of the same radius fixed on one end is melted down and recast into small solid cones, each of radius 3 cm and height 4 cm. How many cones are obtained?

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