The problem involves finding the volume of a solid with a base in the first quadrant, bounded by the x-axis, y-axis, and the line x + 2y = 8. The solid has semicircular cross sections perpendicular to the x-axis.
Some participants have identified misunderstandings in their approaches, particularly regarding the radius of the semicircles. There is acknowledgment of differing interpretations of the cross section, and some have adjusted their reasoning based on feedback from others.
Participants reference an answer key that provides specific volume choices, indicating a potential discrepancy between their calculations and the expected results. There is an ongoing exploration of the correct method to arrive at the solution.
radtad said:The base od a solid is a region in the 1st quadrant bounded by the x-axis, y-axis and the line x+2y=8. If cross sections of the solidperpendicular to the x-axis are semicircles, what is the volume of the solid?
How come the answer isn't just the intgegral from 0-8 of 1/2pi(4-x/2)^2