A balloon, which always remains spherical, has a variable radius. Find the rate at which its volume is increasing with the radius when the later is 10 cm.

Explanation

Let the radius of balloon be r cm.
Formula for the volume of sphere is given by,
V= `4/3pir^3`
Differentiate volume V w.r.t r,
`(dV)/(dr) = d( 4/3 pi r^3 )/dr = 4/3 pi( 3 r^2) =4pi r^2`
Substitute r=`10` cm in the above equation,
`(dV)/(dr) =4pi(10)^2 =400pi  cm^2`
Hence, the volume of the balloon is increasing at a rate of `400pi  cm^2` .