If R is the area enclosed by f(x) and g(x),

Kapalci

Kapalci

Answered question

2022-06-22

If R is the area enclosed by f(x) and g(x), is the volume of the solid generated by revolving R around the x-axis then revolving that solid around the y-axis equal to the volume of the solid generated if the order of the revolutions was switched?

Answer & Explanation

lorienoldf7

lorienoldf7

Beginner2022-06-23Added 19 answers

Apart from the fact that the formulas are different
V = x = a x = b π y 2 d x
V = y = a y = b π x 2 d y
A factor is proximity to the axis of rotation, so if if you think about it intuitively, and consider a small area near x=50 and rotated around the x-axis it would produce a small shape with a small volume. But rotated around the y-axis it would product a large object (because it is relatively far away form the y-axis) and much larger volume

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