The radius of a sphere is changing at the rate of 0.1 cm/sec. The rate of change of its surface area when the radius is 200 cm is

Options

A. `8pi cm^(2)//sec`
B. `12pi cm^(2)//sec`
C. `160pi cm^(2)//sec`
D. `200cm^(2)//sec`

Answer

C

Explanation

Let r be the radius and S be the surface area of the sphere at any time t. Then,
`S=4pir^(2)`
`implies (dS)/(dt)=8pir(dr)/(dt)`
`implies ((dS)/(dt))_(r=200)=8pixx200xx0.1=160 pi cm^(2)//sec`