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# Area, Volume, and Arc Length

# Pyramids, Cones, and Spheres Exercises

### Example 1

Find an integral expression for the volume of a pyramid with height 9 and a square base with side-length 6. Use *h* as the variable of integration, where *h* measures the distance from the base of the pyramid to a slice.

### Example 2

Find an integral expression for the volume of a pyramid with height *h* and a square base with side-length *b*. Evaluate the integral. This will give you a formula for the volume of a pyramid.

### Example 3

Write an integral expression for the volume of an inverted (upside-down) cone with height 5 and base radius 2. Use <em>h</em> (the distance from the base to a slice) as the variable of integration.

### Example 4

Write an integral expression for the volume of a cone with height *h* and base radius *r*. Evaluate your expression to get a formula for the volume of a cone.

### Example 5

Write an integral expression for the volume of a sphere with radius 4. Use horizontal slices and let *h* be the depth of the slice below the top of the sphere.

### Example 6

Write an integral expression for the volume of a sphere with radius *r*. Evaluate your expression to get a formula for the volume of a sphere.