Question 1117082
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.
Area of the side wall = 2πrh
Area of the caps = 2πr^2
Now we differentiate to find the rate of change:
dSWA/dt = (2π)(rdh/dt + hdr/dt) + 4πrdr/dt
dSWA/dt = (2π)(60cm * 8 cm/s + 140cm * 3 cm/s) + (4π)(60cm * 3cm/s) = 7916 cm2/s