Question

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.

Answer 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