The rate of change of surface area of a sphere of radius r when the radius is increasing at the rate of 2 cm/sec is proportional to

Options

A. `1/r`
B. `1/(r^(2))`
C. `r`
D. `r^(2)`

Answer

C

Explanation

Surface area of the sphere is
`S=4pir^(2)` and `(dr)/(dt)=2cms^(-1)`
`:.(dS)/(dt)=4pixx2r(dr)/(dt)=8pixx2=16pir`
`implies(dS)/(dt)propr`