MATH 1172 Quiz: MATH 1172 Ohio State University Quiz 2 Solution

• School: Ohio State University
• Department: Mathematics
• Course: MATH 1172
• Professor: All

Document Summary

Problem 1 [6 points] use the general slicing method to nd the volume of the following solid. The solid whose base is the region bounded by the ellipse cross sections perpendicular to the base and parallel to the x-axis are semicircles. Solution: since the cross section parallel to the x-axis are semicircles and perpendicular to the base, we should integrate cross-sectional area as a function of y with respect to y to nd the volume. The area of a semicircle with radius r is given by 1. Thus we need to nd a formula for the radius of the cross-section at a given value of y. After solving the equation of our curve for x as a function /users/cdavisbuenger/dropbox/teaching/math 1172 fall 2014/quizzes/quizzes. Fa15/solutions/quiz 2 solution. texof y, we have the following two branches of the eclipse: and y2, The diameter of our cross-section travels from the left branch of our ellipse to the right branch of our ellipse.