# Solids of Revolution

Name___________________________

Volume formulas given:

Cylinder: V = (pi)*r^2*h   Cone: (1/3)(pi)*r^2*h   (r = radius, h = height)

Solve the following problems. Assume the units are cm (centimeters) for all problems.

1. The region in the first quadrant bounded by the line 4x + 3y = 12 is rotated about the y-axis. Determine the shape of the solid of revolution and its volume.

Shape:_______________

Volume:______________

2. The region in the first quadrant bounded by the lines y=0, y=5, x=0, and x=2 is rotated about the y-axis. Determine the shape of the solid of revolution and its volume.

Shape:_______________

Volume:______________

3. The region in the fourth quadrant bounded by the line 7x - 4y = 14 is rotated about the x-axis. Determine the shape of the solid of revolution and its volume.

Shape:_______________

Volume:______________

4. The region in the fourth quadrant bounded by the lines y = -2, y = -5, x = 0, and x = 2 is rotated about the y-axis. Determine the shape of the solid of revolution and its volume.

Shape:_______________

Volume:______________

5. The region bounded by 4x + y = 5, x = 0 and y = 1 is rotated about the y-axis. Determine the shape of the solid of revolution and its volume.

Shape:_______________

Volume:______________

## Solids of Revolution ~ extensions

(Some solids may not be cylinders or cones, but volumes can be found using the cylinder or cone volume formulas.)

6. The region bounded by y =3x - 3, x = 3, and y = 0, is rotated about the line x = 3. Determine the shape of the solid of revolution and its volume.

Shape:_______________

Volume:______________

7. The region bounded by y = 2x + 5, x = 0, y = 1, and y = 3 is rotated about the line x = 0. Determine the shape of the solid of revolution and its volume.

Shape:_______________

Volume:______________

8. The region bounded by y = 5, y = 4, x = 0, and x = 4 is rotated about the line y = 0. Determine the shape of the solid of revolution and its volume.

Shape:_______________

Volume:______________

9. The region bounded by y = (-4/3)x + 5, x = 0, and y = (1/3)x, is rotated about the line x = 0. Determine the shape of the solid of revolution and its volume.

Shape:_______________

Volume:______________

10. The region bounded by y = (4/3)x, x = 3, and y = 0, is rotated about the line x = 0. Determine the shape of the solid of revolution and its volume.

Shape:_______________

Volume:______________

J.R.Olsen ~ W.I.U.