A balloon, which always remains spherical, has a variable diameter `3/2(2x+1)`.Find the rate of change of its volume with respect to x.

Explanation

Let the radius of spherical balloon be r.
`:. 2r = 3/2 (2x+1 )`
`rArr r = 3/4 (2x+1)`
and volume ` V = 4/3 pi r^(3)`
` = 4/3 pi *(3/4)^(3) *(2x+1)^(3)`
` = 9/16 pi (2x+1)^(3)`
` :. (dV)/(dx) = 9/16 pi * d/(dx) (2x + 1)^(3)`
`= 9/16 pi * 3 (2x+1)^(2) * 2`
` (27)/8 pi (2x+1)^(2)`