6. O -0.23 points scalcETs 6.3.009. use the method of cylindrical shells to find

Question

6. O -0.23 points scalcETs 6.3.009. use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by the given curves about the x-axis. xy 9, x a 0, y 9, y 11 Need Help? Read 7. O -0.23 points scaloET8 6.3.0 Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by the given curves about the x axis. Need Help? Read It to Tutor 0.120.23 points I Previous Answers scaloET8 6.3.013 Use the method of cylindrical shells to find the volume V of the solid obtained by rotating the region bounded by the given curves about the x-axis. x 3 (y 5)2, x m 12

Explanation / Answer

Solution :(6)

xy = 9, x = 0, y = 9, y = 11

Limits of integration are given by y = 9 and y = 11.

Each shell will have radius R = y
and height h = x = 9/y
and thickness dy, so

V = [a,b] 2 R h dy

   = 2[9,11] (y)(9/y) dy

   = 2[9,11] 9 dy

   = 2(9y) |[9,11]

V = 2(99 - 81) = 36

Solution: (7)

Vx = 2pi*[c;d] y*g(y) dy

Given function is y = x3/2 -----> x = y2/3 , Then;

Vx = 2pi*[0; 8] y* y2/3 dy

     = 2pi * [0; 8] y5/3 dy

     = 2pi *3/8 * y8/3 [0; 8]

     = 3pi/4 * 88/3

     = 3pi/4 * 256

V = 192 pi

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