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You have designed a model of a square-based pyramid in honor of your calculus teacher. The height will be inches. The equation of one side of the pyramid is: .

  1. Sketch a diagram of your pyramid. A complete diagram includes the function, the ‑ and ‑axes, and a typical slice labeled with the appropriate dimensions.

    Pyramids have pointy tips. If the height is inches, the base would start at .

  2. Set up and evaluate an integral that calculates the exact volume of your pyramid.

    Notice that the cross-sections are perpendicular to the -axis, so set up and evaluate an integral in terms of .

Use the eTool below to help solve the problem.
Click the link at right for the full version of the eTool: Calc 8-124 HW eTool