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Triangle Bounded by the Lines y = 0, y = x and x = 4 is Revolved About the X-axis. Find the Volume of The Solid of Revolution. - Mathematics and Statistics

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triangle bounded by the lines y = 0, y = x and x = 4 is revolved about the X-axis. Find the volume of the solid of revolution.

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Solution

Given line is y = x

`V=piint_0^4 y^2dx`

`=pi int_0^4x^2dx`

`=pi/3[x^3]_0^4`

`=(64pi)/3 cubic units.`

Concept: Area of the Region Bounded by a Curve and a Line
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