The diameter of the semi-circles, drawn from the x-axis to the line, will have a length equal to the y-value of the line, -.5x+4. Thus the radius of each semi-circle is -.25x+2. The area of each semi-circle is then .5pi(-.25x+2)^2.
The line has an x-intercept of (8,0), so integrate .5pi(-.25x+2)^2 from 0 to 8 to get approx 16.755.
HTH, Jason Waller Helix Charter HS San Diego, CA
The base of a solid is a region in 1st quadrant bounded by x-axis, y-axis and the line x+2y=8. Cross-sections of the solid perpendicular to the x-axis are semi-circles, what is the volume of the solid. Answer is 16.755--I keep getting a much bigger answer. Any help???