Question:
The surface area of a sphere is the same as the curved surface area of a cone having the radius of the base as 120 cm and height 160 cm. Find the radius of the sphere.
Solution:
Lateral height of cone
$l=\sqrt{(120)^{2}+(160)^{2}}$
$=\sqrt{14400+25600}$
$=\sqrt{40000}$
$=200$
Surface area of sphere = surface area of cone
$4 \pi \mathrm{r}_{1}{ }^{2}=\pi \mathrm{rl}$
$\mathrm{r}_{1}{ }^{2}=\frac{r l}{4}$
$\mathrm{r}_{1}^{2}=\frac{120 \times 200}{4}$
$\mathrm{r}_{1}^{2}=6000$
Radius of sphere
$r_{1}=\sqrt{6000}$
$=77.46 \mathrm{~cm}$