1. ## Related Rates 2

The trunk of a tree is approximately cylindrical in shape and has a diameter of 1 m when height is 15 m. If the radius is increasing at 0.003 m per annum and the height is increasing at 0.4 m per annum, find the rate of increase of the volume of the trunk.

I got 0.145pi m^3/annum. but the answer in my text isn't the same as mine.

My work:

dV/dt=2pi(0.5) (0.003)(15)+pi(0.5)^2(1)(0.4)

2. Originally Posted by skeske1234
The trunk of a tree is approximately cylindrical in shape and has a diameter of 1 m when height is 15 m. If the radius is increasing at 0.003 m per annum and the height is increasing at 0.4 m per annum, find the rate of increase of the volume of the trunk.

I got 0.145pi m^3/annum. but the answer in my text isn't the same as mine.

My work:

dV/dt=2pi(0.5) (0.003)(15)+pi(0.5)^2(1)(0.4)
I did exactly that calculation and got a completely different answer! Try it again.

3. I vote for the OP's value. (Though Captain Black's signature bothers me...)