Question

30 POINTS The radius of a 10 inch right circular cylinder is measured to be 4 inches, but with a possible error of ±0.1 inch. Use linear approximation or differentials to determine the possible error in the volume of the cylinder. Include units in your answer.

Answer 1

dV = ±8π in³

Explanation:

You're given the height, radius, and change in radius (the radius error, dr).

You're asked to find the change in volume (error of the volume, dV).

First write down the equation for the volume of a cylinder.

Derive the volume with respect to the radius (dV/dr) so that you can solve for their changes.

Rearrange the equation to solve for dV.

Plug in your given values.