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Mathematics

A hemisphere of lead of radius 8 cm is cast into a right circular cone of base radius 6 cm. Determine the height of the cone correct to 2 places of decimal.

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Answer

Given,

Radius of hemisphere (r) = 8 cm.

Radius of cone (R) = 6 cm.

Let height of cone be h cm.

Since, hemisphere is casted into cone,

Volume of hemisphere = Volume of cone.

∴23πr3=13πR2h⇒2r3=R2h⇒h=2r3R2⇒h=2×8362⇒h=102436⇒h=28.44 cm.\therefore \dfrac{2}{3}πr^3 = \dfrac{1}{3}πR^2h \\[1em] \Rightarrow 2r^3 = R^2h \\[1em] \Rightarrow h = \dfrac{2r^3}{R^2} \\[1em] \Rightarrow h = \dfrac{2 \times 8^3}{6^2} \\[1em] \Rightarrow h = \dfrac{1024}{36} \\[1em] \Rightarrow h = 28.44 \text{ cm}.

Hence, the height of the cone is 28.44 cm.

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