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Find the approximate formula for the volume of a thin right circular cylindrical shell if r, h, and t denote respectively the radius, length, and thickness.
Solution:
To illustrate the problem, it is better to draw the figure as follows
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| Photo by Math Principles in Everyday Life |
We know that the volume of a right circular cylinder is given by the formula
Take the differential on both sides of the equation, we have
Since the right circular cylinder has a uniform thickness which is t, then it follows that
The above equation becomes
Therefore, the volume of a thin right circular cylindrical shell is
