Question

1. The area A = _r2 of a circular oil spill changes with the radius. At what rate does the area change with respect to the radius when r = 3ft?
6_ ft2/ft
3_ ft2/ft
6 ft2/ft
9_ ft2/ft
2. The height of a cylinder with a fixed radius of 6 cm is increasing at the rate of 3 cm/min. Find the rate of change of the volume of the cylinder (with respect to time) when the height is 20cm.
36_
108_
360_
None of these

Answer 1

1.) A = πr^2
Rate of change (dA/dr) = 2πr.
When r = 3, dA/dr = 2(3)π = 6π ft^2/ft

2.) V = πr^2h
Rate of change of volume given constant r is dV/dt = πr^2dh/dt = π(6)^2(3) = 108π cm^3/min