Math

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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  1. 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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