Estimating the Volume of a Cylindrical Shell

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SUMMARY

The discussion centers on estimating the volume of a cylindrical shell using different radii values. One participant used a radius of 5.5 inches and a differential of 0.5 inches to calculate the change in volume (dV), while another participant referenced a radius of 6 inches, leading to a different estimate. Both approaches are valid for providing an estimate, as the problem allows for variations in radius. It is clarified that the volume of a cylindrical shell was the focus, not a spherical shell.

PREREQUISITES
  • Understanding of calculus concepts, particularly differentiation.
  • Familiarity with the formula for the volume of a cylindrical shell.
  • Knowledge of differential notation and its application in volume estimation.
  • Basic geometry involving cylindrical shapes.
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  • Study the formula for the volume of a cylindrical shell in detail.
  • Learn about the application of differentials in estimating volumes.
  • Explore examples of volume estimation using varying radii.
  • Investigate the differences between cylindrical and spherical volume calculations.
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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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