Question

I needed help having a hard time understanding the review

Answer 1

The volume of the sphere is given by the formula

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

In function notation

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

Find out dV/dt

Remember that

`\begin{gathered} (dV)/(dt)=(dV)/(dr)*(dr)/(dt) \\ \\ (dV)/(dt)=400\pi(ft^3)/(min) \end{gathered}`

Find out dV/dr

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

substitute

`\begin{gathered} 400\pi=(4\pi r^2)(dr)/(dt) \\ \\ (dr)/(dt)=(400\pi)/(4\pi r^2) \\ \\ simplify \\ \\ (dr)/(dt)=(100)/(r^2) \end{gathered}`

Evaluate at r=5 ft

`(dr)/(dt)=(100)/(5^2)=4(ft)/(min)`

therefore

The balloon's radius is increasing at a rate of 4 ft/min