A ball of radius http://webwork.math.uwyo.edu/webwork...f6db721891.png has a round hole of radius http://webwork.math.uwyo.edu/webwork...47b840b231.png drilled through its center. Find the volume of the resulting solid.

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- Oct 7th 2008, 08:06 PMamiv4volume of a sphere with a hole
A ball of radius http://webwork.math.uwyo.edu/webwork...f6db721891.png has a round hole of radius http://webwork.math.uwyo.edu/webwork...47b840b231.png drilled through its center. Find the volume of the resulting solid.

- Oct 7th 2008, 08:14 PMJhevon
this amounts to finding the volume of rotation for the region bounded by the curves $\displaystyle y = \sqrt{144 - x^2}$ and $\displaystyle y = 7$ revolved about the x-axis

or analogously, the region bounded by $\displaystyle y = \sqrt{144 - x^2}$ and $\displaystyle x = 7$ revolved about the y-axis - Oct 7th 2008, 08:39 PMamiv4
so would u set it up like this

2pi*integral from 0 to 9.74679 of sqrt(144-x^2)-7 dx - Oct 7th 2008, 08:43 PMJhevon
- Oct 7th 2008, 08:45 PMamiv4
ya i think im using the washer method. and i thought i was following the formula but guess not

- Oct 7th 2008, 08:53 PMJhevon
- Oct 7th 2008, 09:06 PMamiv4
ya i thought i did that

i just times it by 2 to get rid of the bottom half fo the integral

so it was

2pi*integral from 0 to 9.74679 of sqrt(144-x^2)^2-7^2 dx - Oct 7th 2008, 09:08 PMJhevon