A sphere is expanded to a bigger sphere such that its volume increases by a factor of 64, find the - Maths - Surface Areas and Volumes

Question

A sphere is expanded to a bigger sphere such that its volume
increases by a factor of 64, find the change in its surface area

Manbar Singh · Accepted Answer

Let r1 be the original radius of the sphere
Let r2 be the new radius of the sphere when it is expanded
Now, Now, new volume of sphere = 64 × original volume of sphere⇒43πr23 = 64 × 43πr13⇒r23 = 64r13⇒r2 = 4r1Original surface area of sphere = S1 = 4πr12New surface area of sphere = S2 = 4πr22⇒S2 = 4π4r12⇒S2 = 164πr12⇒S2 = 16S1So, surface area will become 16 times of original

A sphere is expanded to a bigger sphere such that its volume increases by a factor of 64, find the change in its surface area.