Hello, drahcirnaw!

I had tosnakemy 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: .