yEXAMPLE 8Find the volume of a pyramid whose base is a square with side L and whose height is h.SOLUTIONWe place the origin O at the vertex of the pyramid and the x-axis along its central axis as in thefigure. Any plane Py that passes through x and is perpendicular to the x-axis intersects the pyramid in a squarehwith side of length s. We can express s in terms of x by using similar triangles.s/2L/2hLand so s =Video ExampleTutorial. [Another method is to observe that the line OP has slope L/(2h) and so its equation is y =Online TextbookLx/(2h).] Thus the cross-sectional area isA(x)= s :The pyramid lies between x = 0 and x =so its volume ishL2| A (x) drV:h?h2II

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EXAMPLE 8 Find the volume of a pyramid whose base is a square with side L and whose height is h. SOLUTION We place the origin O at the vertex of the pyramid and the x-axis along its central axis as in the figure. Any plane P, that passes through x and is perpendicular to the x-axis intersects the pyramid in a square with side of length s. We can express s in terms of x by using similar triangles. s/2 L/2 ar %3D and so s = Video Example ) Tutorial . [Another method is to observe that the line OP has slope L/(2h) and so its equation is y = Online Textbook Lx/(2h).] Thus the cross-sectional area is A(x) = s' = The pyramid lies between x = 0 and x = , so its volume is V = A (x) dr = h