Question

I am a little confused how should I set up the area equation as Reiman sum

Answer 1

Consider a solid with semi circular base of radius 13. The solid has cross sections parallel to the diameter and perpendicular to the base. Below is the figure. Consider one side of the semi circular let the given radius = x side = 2x (x + x) area of the square will be A = (2x)^2 = 4x^2 Equation of circle is x^2 + y^2 = 169 x^2 + y^2 = 169 x^2 = 169 - y^2 rightarrow (1) Area of cross section delta (y) = 4x^2 = 4 (169 - y^2) from (1) = 676 - 4 y^2 \r\n volume nabla = integral^b_a A (y) middot dy = integral^13_0 (676 - 4y^2) middot dy = [676 y - 4y^3/3]^13_0 = [676 (13) - 4 (13)^3/3] - 0 = 8788 - 8788/3 = 26,364 - 8788/3 = 17576/3 therefore volume of square = 17576/3 cu