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

Question

Mathematics

Jasper

29 August, 00:17

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

+4

Answers (1)

Know the Answer?

Bass · 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