# Thread: Find Volume of Cone

1. ## Find Volume of Cone

A cone of height 24cm has a curved surface area 550 cm2 . Find its volume.

2. It is not too difficult to look up (perhaps on the internet, perhaps in a text) the formula for volume and curved area of a cone of base radius r and height h. The volume is given by $\displaystyle \frac{\pi}{3}r^2h$ and the area by $\displaystyle \pi r l$ where l is the "slant height", the distance from the vertex to the base measured along the curved surface. By the Pythagorean theorem, applied to the right triangle where the legs are the axis of the cone and a radius of the base and the hypotenuse is along the curved surface, $\displaystyle l= \sqrt{r^2+ h^2}$ so that we have $\displaystyle \pi r\sqrt{r^2+ h^2}= 550$.

We are told that the height, h, is 24 so we have $\displaystyle \pi r\sqrt}{r^2+ 24^2}= 550$. solve that for r and use $\displaystyle V= \frac{\pi}{3}r^2(24)$

3. I can take it from here. Thank a lot!

4. I got r = 0, r = 24i and r = -24i. I am stuck here. Can you find the value of r? I can then take it from there.