The edge of a cube was found to be 15 cm with a possible error in measurement of 0.2 cm. Use differentials to estimate the maximum possible error, relative error, and percentage error in computing the volume of the cube and the surface area of the cube. (Round your answers to four decimal places.)
The edge of a cube was found to be 15 cm with a possible error in measurement of 0.2 cm. Use differentials to estimate the maximum possible error, relative error, and percentage error in computing the volume of the cube and the surface area of the cube. (Round your answers to four decimal places.)
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
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Transcribed Image Text:The edge of a cube was found to be 15 cm with a possible error in measurement of 0.2 cm. Use differentials to estimate the maximum possible error, relative error, and percentage error in computing the volume of the cube and the surface area of the cube. (Round your answers to four decimal places.)
Transcribed Image Text:### Understanding Error Calculations in the Surface Area of a Cube
When calculating the surface area of a cube, it is essential to consider possible errors that may arise. Below are the three types of errors you should be aware of:
1. **Maximum Possible Error:**
- This represents the largest possible deviation from the true value of the surface area due to measurement inaccuracies. It's crucial in ensuring that the calculated surface area is as accurate as possible.
2. **Relative Error:**
- This is the ratio of the maximum possible error to the actual measurement of the surface area. It provides insight into the size of the error in relation to the measurement, helping to assess the accuracy of the calculation.
3. **Percentage Error:**
- This is the relative error expressed as a percentage. It gives a clear, intuitive understanding of the error magnitude in proportion to the measurement. This is useful for quickly evaluating the reliability of the surface area calculation.
Each of these error calculations is vital in determining the accuracy and reliability of the surface area measurement of a cube. Understanding and applying these concepts can significantly enhance the precision of your measurements in practical applications.
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