Solution The radius of the solid is given by How to approach the problem: The cross-sectional area is Draw the XYZ axes. Sketch the solid aligned along The limits of the integration are the X-axis. The volume of the solid is given by the definite integral Give the equation for the shape of the solid. Express the cross-sectional QED A x. area as a function of Evaluation the definite integral to find the volume. Example Pyramid with square base H Find the volume of a pyramid of height with a square base with sides of a. length Solution The volume of the solid is given by the definite integral How to approach the problem: A(x) The cross-sections are squares and the area is Draw the XYZ axes. Sketch the solid aligned along the X-axis. The limits of the integration are Express the cross-sectional A x. area as a function of Evaluation the definite integral QED to find the volume.
How to approach the problem: Draw the XYZ axes. Sketch the solid aligned along the X-axis. Give the equation for the shape of the solid. Express the cross-sectional area A as a function of x. Evaluation the definite integral to find the volume. Solution The radius of the solid is given by The cross-sectional area is The limits of the integration are The volume of the solid is given by the definite integral QED How to approach the problem: Draw the XYZ axes. Sketch the solid aligned along the X-axis. Express the cross-sectional area A as a function of x. Evaluation the definite integral to find the volume. Example Pyramid with square base Find the volume of a pyramid of height H with a square base with sides of length a. Solution The volume of the solid is given by the definite integral The cross-sections are squares and the area A(x) is The limits of the integration are QED
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