# Thread: Find height of a cone

1. ## Find height of a cone

Can some one help me with this.

A cone has a volume of 81 Pi cubic inches, and the vertx angle of the verticle cross section is 60 degrees. What is the height of the cone?

2. Originally Posted by SH33
A cone has a volume of 81 Pi cubic inches, and the vertx angle of the verticle cross section is 60 degrees. What is the height of the cone?
First useful fact: If you split the cone into this cross section, you see a triangle. Since it's a cone, the left and right sides must be equal length. What sort of triangle has at least two sides of equal length, and at least one 60 degree angle? (Hint: there aren't a whole lot of other numbers involved in this triangle).

3. Originally Posted by SH33
A cone has a volume of 81 Pi cubic inches, and the vertx angle of the verticle cross section is 60 degrees. What is the height of the cone?
Second useful fact: the formula for the volume of a cone is $V = \frac{1}{3} \pi r^2 h$

Although this doesn't use the length of the side directly, it's very convenient to draw a diagram of the cross section triangle, draw a line representing the height, then figure out formulas for the radius in terms of the side length and height in terms of the side length.

Once you have your r and h in terms of s, substitute them into the cone formula, solve for s.

Now that you have s, you can use your s-to-height formula and find the answer.