Find the instantaneous rate of change of the volume with respect to time.

Question

The radius of a right circular cylinder is given by √(t + 2) and its height is 1/2√t,

where t is time in seconds and the dimensions are in inches. Find the

instantaneous rate of change of the volume with respect to time.

Answer 1

The Volumn of The cylidar is V = π r² h

So, with the given information, V = π (t + 2) (1/2 √t ) ,

V = (π/2 t^3/2 + π t^1/2)

Inst. rate of change = V' = (3π/4) t^1/2 + (π/(2 t^-1/2))