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Considering the volume of a spherical shell as an increment of volume of a sphere, find approximately the volume of a spherical shell whose outer diameter is 8 inches and whose thickness is 1/16 inch.
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 |
If the diameter of a sphere is given in the problem, then the volume of a sphere is
but D = 2R
Since the thickness of a sphere is given and we want to find the volume of a spherical shell, then we have to take the differentials on both sides of the equation. The differential of a volume of a sphere is the same as the volume of a spherical shell.
Substitute the value of R which is ½ D or 4 in. and dR which is 1/16 in. to the above equation, we have
Therefore, the final answer is
