Thread: Volume

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? (п = pie)
A. 64п/3
B. 32п/3
C. 8п/3
D. 4п/3
E. 2п/3

thanks!

Originally Posted by tmd

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? (п = pie)
A. 64п/3
B. 32п/3
C. 8п/3
D. 4п/3
E. 2п/3

thanks!

Hello, tmd,

the semi-circles end at the x-axis and the line y = -1/2x + 2 with y as the diameter of the semi-circles.

Therefore the radius is r = 1/2*y = -1/4x + 1

The volume of the solid is:

V = int from{0} to {4} (pi/2*(-1/4x+1)²)dx = pi/2*int from{0} to{4} (1/16x² - 1/2x + x)dx = pi/2*[1/48x³ - 1/4x² + x]from{0} to{4} = pi/2 * 4/3 = (2pi)/3

So it's answer E

EB