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alexandr402 [8]
2 years ago
11

Use the method of cylindrical shells to find the volume v generated by rotating the region bounded by the given curves about the

specified axis. X = 5y2, y ≥ 0, x = 5; about y = 2.
Mathematics
1 answer:
lys-0071 [83]2 years ago
7 0

The volume of the solid of revolution is \frac{7\pi}{3} cubic units.

<h3>How to find the volume of a solid of revolution with respect to an axis parallel to a Cartesian axis</h3>

The statement has been represented in the image attached below, the formula for the solid of revolution is presented below:

V = \pi \int\limits^{1}_{0} {[5\cdot y^{2}-2]^{2}} \, dy (1)

V = \pi \int\limits^{1}_{0} {(25\cdot y^{4}-20\cdot y +4)} \, dy

V = 25\pi\int\limits^1_0 {y^{4}} \, dy -20\pi\int\limits^1_0 {y^{2}} \, dy +4\pi\int\limits^1_0\, dy

V = \frac{7\pi}{3}

The volume of the solid of revolution is \frac{7\pi}{3} cubic units. \blacksquare

To learn more on solids of revolution, we kindly invite to check this verified question: brainly.com/question/338504

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