Question #c76e4

1 Answer
Antoine
Jul 25, 2015

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

Explanation:

A coin can be looked upon as a small cylinder.

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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#

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