In Exercises 47–50, find the volume of the solid generated by revolv-ing each region about the y-axis. 47. The region enclosed by the triangle with vertices (1, 0), (2, 1), and (1, 1) 48. The region enclosed by the triangle with vertices (0, 1), (1, 0), and (1, 1) 49. The region in the first quadrant bounded above by the parabola y = x2, below by the x-axis, and on the right by the line x = 2 50. The region in the first quadrant bounded on the left by the circle x2 + y2 = 3, on the right by the line x = sqrt(3), and above by the line y = sqrt(3).

In Exercises 47–50, find the volume of the solid generated by revolv-ing each region about the y-axis. 47. The region enclosed by the triangle with vertices (1, 0), (2, 1), and (1, 1) 48. The region enclosed by the triangle with vertices (0, 1), (1, 0), and (1, 1) 49. The region in the first quadrant bounded above by the parabola y = x2, below by the x-axis, and on the right by the line x = 2 50. The region in the first quadrant bounded on the left by the circle x2 + y2 = 3, on the right by the line x = sqrt(3), and above by the line y = sqrt(3).

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter10: Analytic Geometry

Section10.1: The Rectangular Coordinate System

Problem 41E: Find the exact lateral area of each solid in Exercise 40. Find the exact volume of the solid formed...

See similar textbooks

Similar questions

A frustum of a cone is the portion of the cone bounded between the circular base and a plane parallel to the base. With dimensions are indicated, show that the volume of the frustum of the cone is V=13R2H13rh2
Find the exact lateral area of each solid in Exercise 40. Find the exact volume of the solid formed when the region bounded in Quadrant I by the axes and the lines x = 9 and y = 5 is revolved about the a) x-axis b) y-axis
In Exercises 31–32, find the volumes of the solids generated by revolving the regions about the given axes. If you think it would be better to use washers in any given instance, feel free to do so. 31. The triangle with vertices (1, 1), (1, 2), and (2, 2) about a. the x-axis b. the y-axis c. the line x = 10/3 d. the line y = 1 32. The region bounded by y = srqt(x), y = 2, x = 0 about a. the x-axis b. the y-axis c. the line x = 4 d. the line y = 2
In Exercises 51 and 52, find the volume of the solid generated by revolving each region about the given axis. 51. The region in the first quadrant bounded above by the curve y = x2, below by the x-axis, and on the right by the line x = 1, about the line x = -1 52. The region in the second quadrant bounded above by the curve y = -x3, below by the x-axis, and on the left by the line x = -1, about the line x = -2
A rectangular box has three of its faces on the coordinate planes and onevertex in the first octant on the paraboloid z = 4 − x^2 − y^2. Determine themaximum volume of the box.
1. Determine the volume of a solid of revolution generated by rotating around the x-axis the region bounded by the straight lines 3y - x - 3 = o, x = 0, x = 12 and the abscissa axis. 2. Find the volume generated by the region that exists in the first quadrant by the parabola y^2 = 9. the parabola y^2 = 9x and the straight line x = 4.
Find the volume of the solid generated by revolving each region about the y axis. The region enclosed by the triangle with vertices (0, 1), (1, 0) and (1, 1)
How to use the disc method to find the volume of: x^2 - y^2 = 9 and x + y = 9, y=0 and x=0 ? rotates around the x-axis
The volume of the solid obtained by rotating the region enclosed by x=0, y=1, x=y^5 Whats the volume and cubic units?
A region bounded by the parabola y = 4x - x2 and the x-axis is revolved about the x-axis. A second region bounded by the parabola y = 4 - x2 and the x-axis is revolved about the x-axis. Without integrating, how do the volumes of the two solids compare? Explain.