The base radius and height of a right circular cone are measured as 10 cm and 25 cm, respectively, with a possible error in measurement of as much as 0.1 cm in each. Use differentials to estimate the maximum error in the calculated volume of the cone. ( V= 3
The base radius and height of a right circular cone are measured as 10 cm and 25 cm, respectively, with a possible error in measurement of as much as 0.1 cm in each. Use differentials to estimate the maximum error in the calculated volume of the cone. ( V= 3
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter9: Surfaces And Solids
Section9.CR: Review Exercises
Problem 13CR: The radius length of the base of a right circular cylinder is 6 in. The height of the cylinder is 10...
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Step 1
Given formula for the volume of the cone is
Now, the total differential of can be expressed as
Now, we know that and
And there is a possible error in measurement of as much as in each dimension.
This means
And
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