Relation of Rates

Question

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. 

Options:

1. 36π
2. 108π
3. 360π
4. None of these

Answer 1

Kyle, that problem follows a similar pattern as the other ladder problem I just solved, The volume of the cylinder is V(t) = pi*r^2*h(t). Differentiate using the chain rule again, plug in what you know: r = 6 cm, h(t) = 20 cm, and dh/dt = 3 cm/min, and solve for V'(t) which is what the question asked for.

Keeping track of your units can help qualify that you did the right calculations. V'(t) should be what? Cubic centimeters per minute and had better be positive since this cylinder is growing.