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Question 1

Find the volume when the area bounded by the line and the curve are rotated about the x axis.

Question 2

Find the volume when the area bounded by the lines , , and are rotated about the x--axis.

Question 3

Find the volume of revolution when the area bounded by the curve , is rotated about the y-axis.

Question 4

Find the volume of a sphere with a radius of 3 units using the volume by discs method.

Question 5

Question 6

For the following question, find the Volume of the solid that results when the indicated areas are rotated about the x axis.

from to

Question 7

For the following question, find the Volume of the solid that results when the indicated areas are rotated about the x axis.

Question 8

Question 9

For the following question, use technology to find the approximate Volume of the solid that results when the indicated areas are rotated about the y axis.

, ,

Question 10

For the following question, find the Volume of the solid that results when the indicated areas are rotated about the line .

Question 11

Question 12

For the following questions, find the Volume of the solid that results when the indicated areas are rotated about the y-axis.

Question 13

For the following question, find the Volume of the solid that results when the indicated areas are rotated about the y-axis.

Question 14

Question 15

For the following question, find the Volume of the solid that results when the indicated area is rotated about the y-axis.

Question 16

Find the volume when a solid bounded by the curves , , and is revolved around the line .

Question 17

Find the volume when a solid bounded by the curves and and are revolved around the line .

Question 18

Find the volume of a solid created by rotating the area bounded by and are revolved around the y-axis.

Question 19

The region bounded between the curves and is rotated about the line . Using the disc/washer method (i.e. not cylindrical shells), determine the integral used to calculate the volume of the resulting solid. (Note: Set up the integral, but you do not have to evaluate.)

Question 20

Question 21

What is the volume of the solid generated by rotating the area enclosed by , , the x-axis, and , around the x-axis.

Question 22

Find the volume of the solid generated by rotating the region bounded by the x-axis, y-axis, , , and around the x-axis.

Question 23

Find the volume of a damaged cardboard box with a base we can model as the region under the parabola bounded by the y-axis, the x-axis, and , and cross sections perpendicular to the x-axis which are squares.

Question 24

Find the volume of the solid generated by rotating the ellipse about the y-axis.

Question 25

The base of a solid is the region enclosed by the parabola , the line , and the x-axis. If the cross sections perpendicular to the x-axis are squares, find its volume.

Question 26

The base of a solid is the region in the first quadrant enclosed by the graph , and the line . If the cross sections perpendicular to the x-axis are semi-circles, find its volume.

Question 27

The base of a solid is the region enclosed by the graph of , the line , and the y-axis. If the cross sections perpendicular to the y-axis are equilateral triangles, find its volume.

Question 28

The base of a solid is the region in the first quadrant bounded by the x-axis, y-axis and the line .If the cross sections perpendicular to the y-axis are rectangles whose width is half their length (where the length is in the x direction), find its volume.

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