# Determining r2 if a frustum with limited information

• Jul 23rd 2010, 09:09 AM
jkarias
Determining r2 if a frustum with limited information
Hi All,

I've run into a problem with calculating the volume of a frustum and was hoping for some assistance.

I have the following information:

- The slopes are exactly 45°.
- The base must fit on an area exactly 50 meters on a side.
- The height is 10 meters.

R1 and H are easy enough, but I'm not sure how to determine R2. I know the slope angle should help, but I'm not sure how.

j.k.
• Jul 23rd 2010, 09:46 AM
Hello jkarias

Welcome to Math Help Forum!
Quote:

Originally Posted by jkarias
Hi All,

I've run into a problem with calculating the volume of a frustum and was hoping for some assistance.

I have the following information:

- The slopes are exactly 45°.
- The base must fit on an area exactly 50 meters on a side.
- The height is 10 meters.

R1 and H are easy enough, but I'm not sure how to determine R2. I know the slope angle should help, but I'm not sure how.

j.k.

I assume you mean a frustum of a cone, since you refer to R1 and R2. (A frustum can also be a part of a pyramid.)

If you draw a diagram showing a vertical cross-section of the frustum, through the centre of the square, parallel to one of its sides, you'll see that the sloping face of the cone forms an isosceles triangle $(45^o, 45^o, 90^o)$ with the base and a vertical height. Since the height is 10m, the part of the base beneath the sloping face is also 10m. You should be able to see that the radius of the top surface of the frustum is therefore 25 - 10 = 15m.

Can you complete the calculation now?