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

**LauraJane** · Oct4-05, 09:10 PM

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!

**amcavoy** · Oct4-05, 09:57 PM

Originally Posted by LauraJane

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!

You know:

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

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

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

Now minimize this taking into consideration the restraint on volume.