Math Help - Volume by Integration

1. Volume by Integration

A ball of radius 14 has a round hole of radius 9 drilled through its center. Find the volume of the resulting solid.

2. You must use integration?. Then let's use shells to find the volume of the portion removed, then subtract from the volume of the sphere.

$V_{s}=\frac{4}{3}{\pi}(14)^{3}=\frac{10976\pi}{3}$

Now, the volume of the 'hole':

$V_{h}=2{\pi}\int_{0}^{9}x(2\sqrt{196-x^{2}})dx$

= $4\pi\int_{0}^{9}x\sqrt{196-x^{2}}dx$

Integrate and subtract that result from the total volume of the sphere.

You can also use washers to solve this.

3. Originally Posted by Del
A ball of radius 14 has a round hole of radius 9 drilled through its center. Find the volume of the resulting solid.