SOLUTION: DIFF CALC: the height of a right circular cylinder is 50 inches and decreases at the rate of 4 inches per second, while the radius of the base is 20 inches and increases at the rat

Algebra ->  Test -> SOLUTION: DIFF CALC: the height of a right circular cylinder is 50 inches and decreases at the rate of 4 inches per second, while the radius of the base is 20 inches and increases at the rat      Log On


   

Question 1052815: DIFF CALC: the height of a right circular cylinder is 50 inches and decreases at the rate of 4 inches per second, while the radius of the base is 20 inches and increases at the rate of one inch per second. at what rate is the volume changing?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
So first find the volume,
V=pi%2AR%5E2%2AH
Take the derivative with respect to time,
dV%2Fdt=pi%2AR%5E2%28dH%2Fdt%29%2Bpi%2AH%2A2R%28dR%2Fdt%29
dV%2Fdt=pi%2A%28R%5E2%28dH%2Fdt%29%2B2%2AH%2AR%28dR%2Fdt%29%29
Substituting (positive changes increase volume, negative changes decrease volume)
dV%2Fdt=pi%2A%2820%5E2%28-4%29%2B2%2A50%2A20%281%29%29
dV%2Fdt=pi%2A%28-1600%2B2000%29
dV%2Fdt=400piin%5E3%2Fs