Question

Calculate the volume of each muffin cup

Answer 1

Our main goal is to find the volume of the larger cone, and then remove from it the volume of the smaller cone at the bottom.

The volume for a general cone of radius \(r\) and height \(h\) is given by the formula:
\( V = \dfrac{1}{3} \pi r^2 h \)

We immediately hit an obstacle though, because we don't have the height of the whole cone! We're missing the bottom cone's height, which can be added to the other height for the whole cone's height. We'll have to figure it out. Let's look at the cross section through the middle of the cone, which is just a triangle. We draw in the height, and highlight a particular triangle.