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

`l = sqrt((120)^2 +(160)^2)`

`= sqrt(14400 + 25600)`

`= sqrt 40000`

`= sqrt 200`

Surface area of sphere = surface area of cone

\[4 \pi r_1^2 = \pi r l\]

\[ {r_1}^2 = \frac{rl}{4}\]

\[ {r_1}^2 = \frac{120 \times 200}{4}\]

\[ {r_1}^2 = 6000\]

Radius of sphere

`r_1 = sqrt6000`

    `= 77.46 cm`