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A cylindrical drill with radius 4 is used to bore a hole through the center of a sphere of radius...

Question:

A cylindrical drill with radius 4 is used to bore a hole through the center of a sphere of radius 5. Find the volume of the ring shaped solid that remains.

Volumes:

We have used the formula for volume as {eq}\int_{a}^{b} (Area) dx\\ {/eq}

Here dx is the small thickness. Here use the concept of cross-sectional area to find the volume of the given solid.

Answer and Explanation:


Considering the equation of the circle in 2D, we have:

{eq}x^2+y^2=25\\ {/eq}

Now the drill is along the y-axis so, to find the area of the...

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How to Find Volumes of Revolution With Integration

from Math 104: Calculus

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