Volume of a point inside a truncated cone

Hey guys I want to use a 12oz cup to measure things with, but I can't figure out how I would go about doing this. The measurements are roughly 1.1 inch radius at base, 1.6 inch radius on top and 3.8 inch height.

For example, if I wanted to fill it with 4oz of water, how would I calculate what height to fill it at to get this?

Thanks!

Re: Volume of a point inside a truncated cone

You want to use a 12 oz cup to measure things with. The measurements are 1.1 inch at base, 1.6 inch radius and 3.7 inch height.

The formula you're searching for says

Volume = pi/3*h(R^2+R*r+r^2)

where R is the larger radius

Re: Volume of a point inside a truncated cone

I know that, but let's say I want to fill it with 4.5oz of water or something. How would I know what height to fill it to? (without cutting it, etc.)

Re: Volume of a point inside a truncated cone

Quote:

Originally Posted by

**nucci93** I know that, but let's say I want to fill it with 4.5oz of water or something. How would I know what height to fill it to? (without cutting it, etc.)

Since I'm from Europe I gotta love the metric system ;) Use the given formula and solve for the unknown variables. I'll walk you through this:

The formula says

Volume = pi/3*h(R^2+R*r+r^2)

We also know that the relationship between the height and the larger radius (top) is

h/R = 3.7/1.6 <=> h = 3.7R/1.6

In this case we then have

Volume = pi/3*h(R^2+R*r+r^2) => 4.5 = pi/3*h(R^2+R*1.1+1.1^2)

You can solve this equation by first using the above given relationship between R and h into this equation. This will give you only h as unknown to solve for.

Re: Volume of a point inside a truncated cone