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Numerade Educator

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Problem 27 Hard Difficulty

Refer to the figure and find the volume generated by rotating the given region about the specified line.

$ \Re_3 $ about $ OA $

Answer

$\pi$

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Video Transcript

In order to find the volume we know you have to entry along the access parallel to the axis of rotation, which we know The axis of rotation is wyffels zero, giving us an outer radius of axe to the 1/4. Again, this is the distance to the axis of rotation and then the inner radius of X, the distance from Y equals X to the exit irritation. So now we're plugging in. We have the outer which is acts to the 1/4 squared, minus the dinner, which is simply acts squared detox. Simplify this before integrating. Now we can integrate using the power rule, which means increase the exploited by one and divide by the new exponents. Now we can plug in, which gives us our solution of pie divide by three