MAT 302 Assignment Problem 7.3

MAT 302 Assignment Problem 7.3 | Borough of Manhattan Community College

Question 1

(1 point) The volume of the solid obtained by rotating the region enclosed by

y=8x−2x2,y=0y=8x−2x2,y=0

about the y-axis can be computed using the method of cylindrical shells via an integral

Question 2

(1 point) The volume of the solid obtained by rotating the region enclosed by

y=x2,x=2,x=3,y=0y=x2,x=2,x=3,y=0

about the line x=5x=5 can be computed using the method of cylindrical shells via an integral

Question 3

(1 point)

Use the Shell Method to find the volume of the solid obtained by rotating region under the graph of f(x)=x2+2f(x)=x2+2 for 0≤x≤40≤x≤4 about the yy-axis.

Question 4

(1 point) Use the method of cylindrical shells to find the volume generated by rotating the region bounded by the curves y=2+x−x2y=2+x−x2 and y+x=2y+x=2 about the yy-axis. Below is a graph of the bounded region.

Question 5

(1 point) Find the volume of the solid obtained by rotating the region bounded by the given curves about the xx -axis, using the shell method.

x+y=2,x=3−(y−1)2;x+y=2,x=3−(y−1)2;

Question 6

(1 point) The region bounded by y=2+sinxy=2+sin⁡x, y=0y=0, x=0x=0 and 2π2π is revolved about the yy-axis. Find the volume that results.

Question 7

(1 point) 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.

y=x3y=x3, y=0y=0, x=5

Question 8

(1 point) A torus is formed by revolving the region bounded by the circle x2+y2=1x2+y2=1 about the line x=2x=2 (see figure below).