Posted by **Molly** on Tuesday, July 9, 2013 at 10:11am.

Let V be the volume of a pyramid of height 15 whose base is a square of side 5. Part a). Use similar triangles to find the area of the horizontal cross section at a height y. Part b). Calculate V by integrating the crosss-sectional area.

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**MathMate**, Tuesday, July 9, 2013 at 4:33pm
solid: square pyramid

height, h = 15

side of base, s = 5

Area of base, Ab=5^2

area of cross section at height y

=Ab*(y/15)^2

Volume (using the general solid integral formula based on Simpson's rule)

V=(Area at top + Area at base + 4*area at mid-height)*height/6

=(0+25+4*6.25)*height/6

=50*15/6

=125

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