The circumference of a sphere was measured to be 90 cm with a possible error of 0.5 cm. Use differentials to estimate the maximum error in the calculated volume.
Hello, drahcirnaw!
I had to snake my way through this one.
Hope I got it right . . .
The circumference of a sphere was measured to be 90 cm with a possible error of 0.5 cm.
Use differentials to estimate the maximum error in the calculated volume.
We have: .
We are given: . .[1]
We have: .
We are given: . .[2]
The volume of a sphere is: .
. . Then: .
Substitute [1] and [2]: .
Therefore, the maximum error in volume is about: .