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# Exercise 9.9: Volume of a solid obtained by revolving area about an axis

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EXERCISE 9.9

1. Find, by integration, the volume of the solid generated by revolving about the x-axis, the region enclosed by y = 2x2 , y = 0 and x = 1. 2. Find, by integration, the volume of the solid generated by revolving about the x-axis, the region enclosed by y = eŌłÆ2x y = 0, x = 0 and x = 1 3. Find, by integration, the volume of the solid generated by revolving about the y-axis, the region enclosed by x2 = 1+ y and y = 3 . 4. The region enclosed between the graphs of y = x and y = x2 is denoted by R, Find the volume generated when R is rotated through 360┬░ about x-axis. 5. Find, by integration, the volume of the container which is in the shape of a right circular conical frustum as shown in the Fig 9.46.  6. A watermelon has an ellipsoid shape which can be obtained by revolving an ellipse with major-axis 20 cm and minor-axis 10 cm about its major-axis. Find its volume using integration. 1. 4ŽĆ / 5

2. ŽĆ/4 [1ŌłÆ eŌłÆ4]

3. 8 ŽĆ

4. 2ŽĆ/15

5. 14/3 ŽĆm3

6. 1000 ŽĆcm3

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12th Maths : UNIT 9 : Applications of Integration : Exercise 9.9: Volume of a solid obtained by revolving area about an axis | Problem Questions with Answer, Solution