Question

Question #c76e4

Answer 1

`112pi " or " 351.86 cm"/"min`

Explanation:

A coin can be looked upon as a small cylinder.

And its volume is obtained from the formula : `V=pir^2h`

We are asked to find how the volume is changing. This means that we are looking the rate of change of volume with respect to time, that is `(dV)/(dt)`

So all we got to do is to differentiate volume with respect to time, as shown below,

`=>(dV)/(dt)=d(pir^2h)/(dt)=pi(2r*(dr)/(dt)+(dh)/(dt))`

We told that : `(dr)/(dt)=6 cm"/"min` ,
`(dh)/(dt)=4 cm"/"min` , `r=9 cm` and `h=12 cm`

`=>(dV)/(dt)=pi(2(9)*(6)+(4))=112pi~=351.86 cm"/"min`