Q17 of 18 Page 13

A cone of height 24 cm and radius of base 6 cm is made up of modeling clay. A child reshapes it in the form of a sphere. Find the radius of the sphere.

Radius of the base of the cone = 6 cm
Height of the cone = 24 cm ∴ Volume of clay in the cone = π r2h = × π × 6 × 6 × 24 cm3 ∴ Volume of the cone = × π × 6 × 6 × 24 cm3
Let R cm be the radius of the sphere. ∴ Volume of the sphere = π R3 ∴ π R3 = × π × 6 × 6 × 24 ⇒ 4 π R3 = π × 6 × 6 × 24
Þ R3 =
     = 63 ∴ R = 6 cm ∴ Radius of the sphere = 6 cm.

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