#### Question

A hemisphere of lead of radius 7 cm is cast into a right circular cone of height 49 cm. Find the radius of the base.

#### Solution

Given radius of hemisphere = 7cm = `r_1`

Height of cone h = 49cm

Volume of hemisphere = Volume of cone

⇒ `2/3πr_1^3 = 1/3πr_2^2h`

⇒ `2/3xx7^3=1/3r_2^2xx49`

⇒ `(2xx7xx7xx7xx3)/(3xx49)=r_2^2`

⇒`r_2^2=3.74cm`

∴ Radius of the base =3.74cm.

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Solution A Hemisphere of Lead of Radius 7 Cm is Cast into a Right Circular Cone of Height 49 Cm. Find the Radius of the Base. Concept: Volume of a Sphere.