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Finding the Volume of a Solid In Exercises 23 and 24, use the disk method or the shell method to Find the volumes of the solids generated by revolving the region bounded by the graphs of the equations about the given lines.
(a) the x-axis
(b) the y-axis
(c) the line
(d) the line
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Chapter 7 Solutions
Calculus: Early Transcendental Functions
- Find the volumes of the solids generated by revolving the regions bounded by the graphs of the equations about the given lines. y = Vx y = 0 X = 3 (a) the x-axis (b) the y-axis (c) the line x = 3 (d) the line x = 9 Need Help? Read It Submit Answerarrow_forwardFind the volumes of the solids The solid lies between planes perpendicular to the x-axis at x = 0 and x = 1. The cross-sections perpendicular to the x-axis between these planes are circular disks whose diameters run from the parabola y = x2 to the parabola y = sqrt(x).arrow_forwardFinding the Volume of a Solid In Exercises 17-20, find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the line y = 4.y =1/2x3, y = 4, x = 0arrow_forward
- Find the volume of the solid enclosed by the paraboloid z = 3 + x² + (y - 2)2 and the planes z = 1, x = -2, x = 2, y = 0, and y = 2. Need Help? Read It Watch Itarrow_forwardFind the volume of the solid generated by revolving the region enclosed by the triangle with vertices (2,3), (2,6), and (7,6) about the y-axis. The volume of the solid generated by revolving the region enclosed by the triangle with vertices (2,3), (2,6) and (7,6) about the y-axis is cubic units. (Type an exact answer, using a as needed.)arrow_forwardy = 2. Find the volumes of the solids generated by revolving the triangle with vertices (2,2), (2,8), and (5,8) about (a) the x-axis, (b) the y-axis, (c) the line x= 7, and (d) the line a. The volume of the solid generated by revolving about the x-axis is cubic units. (lype an exact answer, using t as needed, or round to the nearest tenth.)arrow_forward
- Find the volumes of the solids The base of the solid is the region bounded by the parabola y2 = 4x and the line x = 1 in the xy-plane. Each cross-section perpendicular to the x-axis is an equilateral triangle with one edge in the plane. (The triangles all lie on the same side of the plane.)arrow_forwardUsing geometry, calculate the volume of the solid under z 64 -T2-y2 and over the circular disk x2 y 64arrow_forwardonsider the tetrahedron (a 4-sided pyramid whose faces are all triangles) with vertices atA = (1, 0, 0), B = (0, 2, 0), C = (0, 1, 3), and D = (2, 2, 0). Calculate the surface area and the volumeof the tetrahedron.(Hint: You may use the fact that the volume a tetrahedron is exactly one-sixth ofthe volume of the parallelepiped generated by the same vectors.) Surface Area = Volume =arrow_forward
- Direction: Find the volume of the solid of revolution formed by revolving a plane region about a given line or axis. 1. Determine the volume of the solid generated by revolving about the x-axis the region bounded by the curve y = x3, the x-axis and the line x = 2. The region bounded by the curve y = x² - 2 and the lines y = -2 and x = 2 is rotated about the line y = -2. Calculate the volume of the solid formed. 2.arrow_forwardFind the volumes of the solids generated by revolving the regions bounded by the graphs of the equations about the given lines. y = x? y = 6x – x2 (a) the x-axis (b) the line y = 10arrow_forwardFind the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y = In(3x), y = 1, y = 3, x = 0; about the y-axis Robe V = Sketch the region. y y y 4 6 6- 4 2 2 4 6 2 4 6 -1 4 Sketch the solid and a typical disk or washer. Graph Graph Description Graph Graph Description Graph Graph Description -6 -5 -4 -3 -2 -1T 2 3 4 5 6 -6 -5 -4 -3 -2 -1- 22 3 4 5 6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 Activate Winde Go to Settings to a -4arrow_forward
- Elementary Geometry For College Students, 7eGeometryISBN:9781337614085Author:Alexander, Daniel C.; Koeberlein, Geralyn M.Publisher:Cengage,Calculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,