# Homework Help: Volume of a cone is 10 cubic cm

1. Oct 4, 2005

### LauraJane

volume of a cone is 10 cubic cm....

Q: a cone shaped paper drinking cup holds 10 cubic cm of water. We would like to find the height and radius that will require the least amount of paper.

Volume of a cone is: (b x h)/3, or with radius is: ((pi r squared x h))/3.

I think you solve this problem by finding a ratio and getting h in terms of r. Any ideas? Thank you!

2. Oct 4, 2005

### amcavoy

You know:

$$\text{V}=\frac{\pi\,r^{2}\,h}{3}=10$$

If I remember correctly, the surface area (what you want to minimize) is:

$$\text{S}=\pi\,r\,\sqrt{r^{2}+h^{2}}$$

Now minimize this taking into consideration the restraint on volume.

Last edited: Oct 4, 2005