# circumscribing sphere

## Volume of pyramid cut from a sphere

**Problem**

The diameter of a sphere is 18 in. Find the largest volume of regular pyramid of altitude 15 in. that can be cut from the sphere if the pyramid is (a) square, (b) pentagonal, (c) hexagonal, and (d) octagonal.

## 016 Radius of the sphere circumscribing a regular triangular pyramid

**Example 016**

Find the area of the surface and the volume of the sphere circumscribed about a regular tetrahedron of edge 25 cm. See Figure 015.

## 013 Insciribed and circumscribed sphere about a cube - volume comparison

**Example 013**

Compare the volume of a sphere inscribed in a cube with volume of the sphere that circumscribes the cube.

## 012 Sphere circumscribed about a right circular cylinder

**Example 012**

Find the volume and total area of the sphere which circumscribes a cylinder of revolution whose altitude and diameter are each 6 inches.