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Home > CALC > Chapter 8 > Lesson 8.3.3 > Problem 8-123


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 will include 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 the integral that will find 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 8-123 HW eTool (Desmos)