A solid shape described as the region bounded by revolved around the y-axis, needs to have 1/4 of its volume trimmed off to meet a weight restriction. This will be done by reducing the radius of the piece - in other words, the resulting shape will be described as above, but with the region also bounded by x = q. Find the resulting radius, q.

Question

A solid shape described as the region bounded by  revolved around the y-axis, needs to have 1/4 of its volume trimmed off to meet a weight restriction. This will be done by reducing the radius of the piece - in other words, the resulting shape will be described as above, but with the region also bounded by x = q. Find the resulting radius, q.

Quizplus · Accepted Answer

Since we need to remove 1/4th of the volume, the new volume will be 3/4 of the original volume. 
Let the original radius of the solid be r and the height be h, then the original volume of the solid will be πr^2h. 
After trimming, the new solid will have a radius of q and the same height h. 
The new volume will be 3/4 of the original volume, i.e., 
(3/4)πr^2h = πq^2h 
Simplifying, we get 
q = r/√(3/4) = r/√(3)/2 = 2r/√3 
Therefore, the answer is B.

A Solid Shape Described as the Region Bounded by