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Area, Volume, and Arc Length

Area, Volume, and Arc Length

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.

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