Question

The surface area of a sphere of radius 5 cm is five times the area of the curved surface of a cone of radius 4 cm. Find the height of the cone.

Answer 1

Radius of a sphere $\left(r\right)=5cm$

$\therefore Surfacearea=4\pi r^2$

$=4\pi \times 5\times 5=100\pi c{m}^2$

Radius of cone $\left(r_1\right)$ = 4 cm

Curved Surface $=\frac{100\pi }{5}c{m}^2$

$=20\pi c{m}^2$

$\therefore$ $Slantheight\left(l\right)=\frac{Area}{\pi r}$

$=\frac{20\pi }{\pi \times 4}$ = 5cm

Now height (h) $=\sqrt{l^2-r^2}$

$=\sqrt{(5{)}^2-(4{)}^2}=\sqrt{25-16}cm$

$\sqrt{9}=3cm$