Estimating the Volume of a Cylindrical Shell

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The discussion focuses on estimating the volume of a cylindrical shell using different radius values. One participant calculated the change in volume using a radius of 5.5 inches and a differential of 0.5 inches, while another used a radius of 6 inches, resulting in different volume estimates. It is clarified that both approaches can yield valid estimates since the problem is seeking an approximation. The confusion arises from the incorrect application of the volume formula for a spherical shell instead of a cylindrical one. Ultimately, both methods are acceptable for estimating volume in this context.
mopit_011
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Homework Statement
Estimate the volume of material in a cylindrical shell with length 30 inches, radius 6 inches, and shell thickness 0.5 inches. (Hint: Use differential estimates to solve the problem.)
Relevant Equations
dV = (4*pi)*r^2*dr
Using the equation above, I plugged in 5.5 inches for the radiu and 0.5 inches for the value of dr and then solved for the estimate of the change in volume, dV. However, the solution instead uses a value of 6 inches for the radius receiving a different estimate for the problem than I did. Is my solution incorrect or would both approaches work since the problem is asking for an estimate?
 
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You have used the volume of a spherical shell, not a cylindrical one.

As to which radius to use, both would give an estimate.
 

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