Textbook Problem

In Exercises 44 and 45, use the formula from Exercise 43. Similar triangles were used to find h and H.

A container of yogurt has the shape of a frustum of a cone. With the lower base having diameter length $6$ cm and the upper base having diameter length $8$ cm, the volume of such a container $7.5$ cm tall can be determined by using $H=30$ cm and $h=22.5$ cm. Find its volume.

A frustum of a cone is the portion of the cone bounded between the circular base and a plane parallel to the base. With dimensions are indicated, show that the volume of the frustum of the cone is

$V=\frac{1}{3}\pi R^{2}H-\frac{1}{3}\pi rh$