The surface area of a sphere is 2464 cm2. If its radius be doubled, what will be the surface area of the new sphere?
Let the radius of sphere be ‘r’ cm
Surface area of sphere = 2464 cm2
Surface area of sphere is given by 4πr2
∴ 4πr2 = 2464 cm2
⇒ 4 × 22/7 × r2 = 2464 cm2
⇒ r2 = 2464 × 1/4 × 7/22 cm2 = 196 cm2
⇒ r = 14 cm
Radius of new sphere is double the radius of given sphere.
Let the radius of new sphere be r’ cm
∴ r’ = 2r
r’ = 2 × 14 cm = 28 cm
Surface area of new sphere = 4πr’2
= 4 × 22/7 × 282 cm2
= 9856 cm2
∴ Surface area of new sphere is 9856 cm2.