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.

Answer 1

Radius of the spherical cannonball, R = 14 cm
Radius of the base of the cone, r = 17.5 cm
Let h cm be the height of the cone.
Now, volume of the sphere = volume of the cone
$$\begin{gathered} \Rightarrow \frac{4}{3}\mathrm{\pi }{R}^3=\frac{1}{3}\mathrm{\pi }{r}^{\mathit{2}}h \\ \Rightarrow 4\times {14}^3={\left(17.5\right)}^2\times h \\ \Rightarrow h=\frac{4\times 14\times 14\times 14}{17.5\times 17.5}=35.84\mathrm{cm} \end{gathered}$$

∴ The height of the cone is 35.84 cm.