Calculus - Related Rates

Question

The radius of a right circular cylinder is increasing at the rate of 485 in/s , while the height is a constant 2/5 inches making the formula for volume, V=2/5πr² , At what rate is the volume of the cylinder changing when the radius is 5 in?

Answer 1

Let's have first the formula for the volume of a right cylinder:

V= π r² h

Since the height is a constant 2/5 inches, we have verified the volume:

V = (2/5) π r²

Derive both sides of the equation with respect to time (t):

dV/dt = (4/5) π r (dr/dt)

when: dr/dt = 485 in./sec, r = 5 in.:

dVdt = (4/5) π (5) (485)

dVdt = 1940 π

dVdt ≅ 6094.69 in³/sec