Question

While building a snowman, a large snowball is created so that the radius is changing at the rate of 5 inches per hour. How fast is the volume of the snowball changing at the instant the snowball has a radius of 10 inches?

Answer 1

Answer:

2000π in³/s

or 6283.2 in³/s

Step-by-step explanation:

dr/dt = 5  

volume of sphere is given as

v = (4/3)(π)r³

differentitate wrt r

dv/dr = 3×4/3 ×π×r²

dv/dr = 4πr²

put r = 10

dv/dr = 4π(10)²

dv/dr = 400π

by chain rule

dv/dt = dv/dr ×dr/dt

dv/dt = 400π× 5

dv/dt = 2000π in³/s

or dv/dt =6283.2 in³/s