A spherical cannonball 28 cm in diameter is melted and cast into a right circular cone would,

Question:

A spherical cannonball 28 cm in diameter is melted and cast into a right circular cone would, whose base is 35 cm in diameter. Find the height of the cone.

Solution:

Radius of the spherical cannonball, = 14 cm

Radius of the base of the cone, = 17.5 cm
Let h cm be the height of the cone.
Now, volume of the sphere = volume of the cone

$\Rightarrow \frac{4}{3} \pi R^{3}=\frac{1}{3} \pi r^{2} h$

$\Rightarrow 4 \times 14^{3}=(17.5)^{2} \times h$

$\Rightarrow h=\frac{4 \times 14 \times 14 \times 14}{17.5 \times 17.5}=35.84 \mathrm{~cm}$

∴ The height of the cone is 35.84 cm.

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