- #1

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## Homework Statement

Find the volume bounded between the sphere of radius a centered at (0,0,0) and the cone z=sqrt(x

^{2}+y

^{2}).

## The Attempt at a Solution

So, subbing our definition for z into the the equation for a sphere of radius a centered at (0,0,0):

2x

^{2}+ 2y

^{2}= a

^{2}. Converting to cylindrical coordinates,

2r

^{2}= a

^{2}

r = a/sqrt(2). I use the bounds,

0≤z≤a

0≤θ≤2*pi

0≤r≤a/sqrt(2)

I use 1*r as my integrand to find volume and I get a

^{3}*pi/2. Am I doing this right?