Question

The radius of a circular disk is given as 28 cm with a maximum error in measurement of .4 cm. Use differentials to estimate the maximum possible error in the calculated area of the disk.
What is the relative error?

Answer 1

well the maximum radius would be 28.4 cm

minumum radius would be 27.6 cm

use theese values to find the difference in the areas.

Answer 2

which would be 140.7433509 so where do i go from there

Answer 3

well isn't relative error the absolute error divided by the measurement expressed as a percentage.

so what is the area when r = 28

and perhaps relative error is 140. 7/(Area) * 100

thats my best guess

Answer 4

From
\[A=πr^2 \]
find dA/dr:
\[\frac{dA}{dr}=2πr\]
so
\[dA=2πrdr \]
where dr is the error in the radius and so dA is the error in the area. dr will be 0.4 since the error is plus or minus 0.4cm.

Answer 5

And r is the radius, 28cm. To find relative error, just find: \[\frac{ dA }{A} = ?\] and \[A = \pi r^2 \] (where r=28cm)