Question

Suppose that the radius is expanding at a rate of 0.6 inches per second. How fast is the volume changing when the radius is 2.8 inches? Use at least 5 decimal places in your answer.

Answer 1

59.11221 in^3/s

Explanation:

Given dr/dt = 0.6 in/s

Find dV/dt when r = 2.8 in.

`V=(4\pi r^3)/(3)\\`

so
`(dV)/(dr)=4\pi r^2\\`

`(dV)/(dt)=(dV)/(dr)\cdot(dr)/(dt)=4\pi r^2\cdot(dr)/(dt)`

Use r = 2.8 in and dr/dt = 0.6 in/s

get

`(dV)/(dt)=59.11221 in^3/s`