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 Aurica June 9th, 2009 06:44 PM

A Cylindrical hole

A Cylindrical hole is drilled through the center of a sphere of radius R. Use the method of cylindrical shells to find the volume of the remaining solid, given that the solid is 6 cm high.

V = 4? ? x ?(R² - x²) dx ..... from ?(R² - (3)²) to R
= -4?/3 (R² - x²)^(3/2) ..... from ?(R² - (3)²) to R
= 36 ?

Are these correct? Thank you

 Scott June 9th, 2009 07:05 PM

Re: A Cylindrical hole

Your answer looks correct, and I again apologize for another mistake in which I claimed that $\sqrt{R^2\,-\,r^2}\,=\,6\,\mbox{cm}$.

 skipjack June 10th, 2009 02:57 PM

$36\pi\text{ cm}^{\small{3}}$

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