# Thread: Confusing related rates problem

1. ## Confusing related rates problem

This problem has me extremely confused, would really appreciate some help..

A right circular cone and a hemisphere have the same base, and the cone is inscribed in the hemisphere. The figure is expanding in such a way that the combined surface area of the hemisphere and its base is increasing at a constant rate of 18 square inches per second. At what rate is the volume of the cone changing at the instan when the radius of the common base is 4 inches?

As i said, im extremely confused and have nothing....Thanks in anyone can help!!

2. Originally Posted by alakaboom1
This problem has me extremely confused, would really appreciate some help..

A right circular cone and a hemisphere have the same base, and the cone is inscribed in the hemisphere. The figure is expanding in such a way that the combined surface area of the hemisphere and its base is increasing at a constant rate of 18 square inches per second. At what rate is the volume of the cone changing at the instan when the radius of the common base is 4 inches?

As i said, im extremely confused and have nothing....Thanks in anyone can help!!
surface area of hemisphere and base ...

$\displaystyle A = 2\pi r^2 + \pi r^2 = 3\pi r^2$

$\displaystyle \frac{dA}{dt} = 6\pi r \frac{dr}{dt}$

you are given values for $\displaystyle r$ and $\displaystyle \frac{dA}{dt}$, find $\displaystyle \frac{dr}{dt}$

volume of the cone (note height of cone is r of hemisphere) ...

$\displaystyle V = \frac{\pi}{3} r^3$

$\displaystyle \frac{dV}{dt} = \pi r^2 \frac{dr}{dt}$

evaluate $\displaystyle \frac{dV}{dt}$

3. ahhh.....i see. i failed to realize that h was equal to r. Thank you so much.