__Category__: Differential Calculus, Solid Geometry"Published in Newark, California, USA"

The altitude of a certain right circular cone is the same as the radius of the base, and is measured as 5 inches with a possible error of 0.02 inch. Find approximately the percentage error in the calculated value of the volume.

__Solution:__

From the description of a problem, it is an approximation and error problem because it involves the difference of the dimensions of a right circular cone as well as the difference of the volume.

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The volume of a right circular cone is calculated as

but r = h

Take the differentials on both sides, we have

The original volume of the right circular cone is calculated as

Therefore, the percent of error is calculated as

% Error = (± 0.012)(100) =

**1.2%**