Webwork 10 problems on Arc length and Volumes of Revolution

Fahad Khaleefoh M145Haruta Assignment Volumes of Revolution due 03/13/2017 at 08:00am EDT

1. (1 point) Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. Sketch for yourself the region, the solid, and a typical disk or washer.

y = 8x2,x = 1,y = 0, about the x-axis

Answer(s) submitted: • pi(64*1ˆ5)/5

(correct)

2. (1 point) Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. Sketch for yourself the region, the solid, and a typical disk or washer.

y = x2,y = 0,x = 3, about the y-axis

Answer(s) submitted: • pi*9ˆ2/2

(correct)

3. (1 point) Find the volume of the solid formed by rotating the region inside the first quadrant enclosed by y = x2

y = 5x about the x-axis.

Answer(s) submitted: • pi(25(5)ˆ3/3-(5)ˆ5/5)

(correct)

4. (1 point) Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. Sketch for yourself the region, the solid, and a typical disk or washer.

y = x2,y2 = x about the y-axis

Answer(s) submitted: • pi*(1ˆ2/2-1ˆ5/5)

(correct)

5. (1 point) Find the volume of the solid obtained by rotating the region bounded by the given curve about the specified axis.

x2 +(y−8)2 = 49 about the y-axis.

Volume =

Answer(s) submitted: •

(incorrect)

6. (1 point) Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line.

x = 1− y4, x = 0; about x = 1.

Volume =

Answer(s) submitted: •

(incorrect)

7. (1 point) The region in the first quadrant bounded by y = 3x2 , 2x + y = 5, and the y-axis is rotate about the line x =−2. The volume of the resulting solid is:

Answer(s) submitted: •

(incorrect)

8. (1 point) Find the volume of the solid obtained by rotating the region bounded by

y = x4,y = 1;

about the line y = 3

Answer:

Answer(s) submitted: •

(incorrect)

9. (1 point) The region between the graphs of x = y2 and x = 6y is rotated around the line y = 6.

The volume of the resulting solid is: Answer(s) submitted:

• (incorrect)

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