Estimating the Volume of a Cylindrical Shell

[mopit_011]

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?

 

[Orodruin]

You have used the volume of a spherical shell, not a cylindrical one.

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