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.

Answer 1

Lateral height of cone

Surface area of sphere = surface area of cone

$$\begin{gathered} 4{{\mathrm{\pi r}}_1}^2=\mathrm{\pi rl} \\ {{\mathrm{r}}_1}^2=\frac{rl}{4} \\ {{\mathrm{r}}_1}^2=\frac{120\times 200}{4} \\ {{\mathrm{r}}_1}^2=6000 \end{gathered}$$

Radius of sphere