calculus question

Question

The radius of a right circular cylinder is given by √(t+7) and its height is 1/7√t , where t is time in seconds and the dimensions are in inches. Find the rate of change of the volume of the cylinder, V, with respect to time.(Volume(V) of a cylinder with a circular base area (A) and hight (h) is given by V=Ah).

Answer 1

V = Ah = π r² h = π (√(t + 7))² ((1/7)√(t)) = π (t + 7) (1/7) t^1/2 = π ((1/7)t^3/2 + t^1/2)

V' = π ((1/7)(3/2)t^1/2 + (1/2)t^-1/2) = π ((3/14)√t + (1/2√t))