1. The problem statement, all variables and given/known data(adsbygoogle = window.adsbygoogle || []).push({});

k so here is the equation i need help with that will find me the volume of a sphere

2*pi*y*sqrt(25-(y-1)^2) dy - 5*pi from 0 to 6

the 5 pi is the volume of a cylinder

2. Steps

so first i subbed u=y-1

took the 2 pi out of the integral

that got me 2 integrals u*sqrt(25-(u)^2) du + sqrt(25-(u)^2) du

the first integral = (2*pi*24^(3/2))/3

the second i used a trig sub and my final answer is

(25pi^2)/2 +

-25*asin(-.2)+sqrt(24)

3. Answer

the answer is suppose to be 25pi^2 + 500pi/3

i got 25pi^2 + (-75*asin(-.2)+3*sqrt(24)+2*(24)^(3/2) -15)/3

which is approx

25pi^2 + 499.89pi/3

how do i get the exact answer

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# Homework Help: Finding volumes by rotating around an axis of revolution

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