Ring of the Lord

Calculus Level 3

A ring shaped solid is formed when the circle with the equation ( x − 12 ) 2 + ( y − 16 ) 2 = 4 (x-12)^{2}+(y-16)^{2}=4 is revoluted with y = − x y=-x as its axis of revolution with center at origin. Find the volume of the ring shaped solid formed.

Clarification: Enter the answer by correcting it to three decimal places.


The answer is 1579.137.

Abhay Tiwari by Abhay Tiwari , 28, India

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1 solution

Otto Bretscher
Apr 28, 2016

The point on the axis closest to the circle is ( − 2 , 2 ) (-2,2) , by inspection, so that the volume is

V = V= (area of circle)(distance traveled by the circle's center)= ( 4 π ) ( 2 π 14 2 ) ≈ 1563 (4\pi)(2\pi 14\sqrt{2})\approx \boxed{1563}

0 Helpful 0 Interesting 0 Brilliant 0 Confused

Sir, is 14√2 correct? I think it should be 20 by Pythagorean theorem.

Abhay Tiwari - 5 years, 1 month ago

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The path of the centroid is a circle with its center at ( − 2 , 2 , 0 ) (-2,2,0) , not at the origin.

Otto Bretscher - 5 years, 1 month ago

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Ok, got it. Sir, can you check [this](Sir, please have a look at this , please tell if some ambiguity arises.

Abhay Tiwari - 5 years, 1 month ago

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@Abhay Tiwari – I'm busy at work now, but will check in the evening.

Otto Bretscher - 5 years, 1 month ago

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