Homework SourseThe base of a solid is the region in the first quadrant boun
The base of a solid is the region in the first quadrant bounded by the line x + 2y = 4 and the coordinate axes. What is the volume of the solid if every cross-section perpendicular to the x-axis is a semicircle?
Solution
This can be solved by volume of cone x intercept = the Height of cone y intercept = the diameter of the base when x=0 : y = 2 when y = 0: x= 4 H = 4 R = D/2 = 1 Volume = (1/2) Volume Volume = (1/2) 1/3 (pi)(R)^2 (H) V = (1/2) 1/3 (pi)(1)^2 (4) V = 4pi/6 V = 2 pi/3
