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A measuring instrument has a 1% error, that is, if a length measures 100mm, it has an error of ±1mm. The radius of a sphere is measured with such instrument as 50mm. Calculate (to the closest mm³) the Volume of this sphere? Volume = mm³ Using the "small change formula", calculate (to the closest mm³) the approximate change in the Volume = ± mm³ What is the percentage error in the Volume given the formula below? % The percentage error in the volume ΔΙ' V x 100 %

A measuring instrument has a 1% error, that is, if a length measures 100mm, it has an error of ±1mm. The radius of a sphere is measured with such instrument as 50mm. Calculate (to the closest mm³) the Volume of this sphere? Volume = mm³ Using the "small change formula", calculate (to the closest mm³) the approximate change in the Volume = ± mm³ What is the percentage error in the Volume given the formula below? % The percentage error in the volume ΔΙ' V x 100 %

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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A measuring instrument has a 1% error, that is, if a length measures 100mm, it has an error of ±1mm. The radius of a sphere is measured with such instrument as 50mm. Calculate (to the closest mm³) the Volume of this sphere? Volume = mm³ Using the "small change formula", calculate (to the closest mm³) the approximate change in the Volume = ± mm³ What is the percentage error in the Volume given the formula below? % The percentage error in the volume ΔΙ' V -x 100 %
Transcribed Image Text:A measuring instrument has a 1% error, that is, if a length measures 100mm, it has an error of ±1mm. The radius of a sphere is measured with such instrument as 50mm. Calculate (to the closest mm³) the Volume of this sphere? Volume = mm³ Using the "small change formula", calculate (to the closest mm³) the approximate change in the Volume = ± mm³ What is the percentage error in the Volume given the formula below? % The percentage error in the volume ΔΙ' V -x 100 %
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Step 1: Introduction of the given problem

The radius of the sphere is 50 space m m and the error in the measuring instrument is 1 percent sign.

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