Mensuration-20

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A solid cone is 27 cm high and the radius of its base is 6 cm. Three such cones
are melted and recast into a solid sphere.
Determine the diameter of the sphere.

Solution: For solid cone, r = 6 cm, h = 27 cm

Volume of the cone = 1/3 π r2 h = 1/3 x 22/7 x 6 x 6 x 27 cu. cm

Volume of 3 cones = 3 x 1/3 x 22/7 x 6 x 6 x 27 cu. cm

If the radius of the sphere is R then volume of the sphere

= 4/3 π R3 = 22/7 x 6 x 6 x 27

R3 = 22/7 x 6 x 6 x 27 x 7/22 x 3/4 = 9 x 9 x 9

Therefore, R = 9 cm.

Diameter = 2 R = 18 cm

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