What is required to calculate the volume of a frustum?

To find the volume of a frustum, which is essentially a truncated cone (a cone with the top cut off), you need to consider the relationship between the original cone and the smaller cone that is removed from it. The frustum is formed by subtracting the volume of the smaller, upper cone from the volume of the original, larger cone.

The volume of a cone can be calculated using the formula ( V = \frac{1}{3} \pi r^2 h ), where ( r ) is the radius of the base and ( h ) is the height. By applying this formula, you first calculate the volume of the entire original cone. Then, you find the volume of the smaller cone that has been removed, which also requires knowing its radius and height.

By taking the volume of the original cone and subtracting the volume of the removed cone, you obtain the volume of the frustum. This makes sense conceptually: you're effectively measuring only the remaining portion after the smaller cone has been cut off.

This is why the correct choice is to calculate the volume of the original cone minus the volume of the removed cone. This method is essential for accurately determining the volume of the frustum in three-dimensional geometry.