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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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