document.write( "Question 1117082: A balloon, in the shape of a right circular cylinder, is being inflated in such a way that the radius and height are both increasing at the rate of 3 cm/s and 8 cm/s, respectively. What is the rate of change of total surface area when its radius and height are 60 cm and 140 cm, respectively? \n" ); document.write( "

Algebra.Com's Answer #732101 by addingup(3677) $\"\"$ $\"About$

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The increase in radius increases the area of the caps and the area of the side wall. The increase in height increases the area of the side wall.
\n" ); document.write( "Area of the side wall = 2πrh
\n" ); document.write( "Area of the caps = 2πr^2
\n" ); document.write( "Now we differentiate to find the rate of change:
\n" ); document.write( "dSWA/dt = (2π)(rdh/dt + hdr/dt) + 4πrdr/dt
\n" ); document.write( "dSWA/dt = (2π)(60cm * 8 cm/s + 140cm * 3 cm/s) + (4π)(60cm * 3cm/s) = 7916 cm2/s \n" ); document.write( "

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