Hello, kwivo!

Since , we have: . cmThe circumference of a sphere was measured to be 88 cm with a possible error of 0.5 cm.

We are told that: . cm

(a) Use differentials to estimate the maximum and relative error

in the calculated surface area.

(Round maximum error to the nearest whole number

and relative error to three decimal places.)

Surface area: .

The base sphere has area: . cm².

The approximate error in the area is: .

Hence: .

The maximum error is: . cm²

The relative error is: .

(b) Use differentials to estimate the maximum and relative error

in the calculated volume.

(Round maximum error to the nearest whole number

and relative error to three decimal places.)

Volume of a sphere: .

The base sphere has volume: . cm³

The approximate error in the volume is: .

Hence: .

The maximum error is: . cm³

The relvative error is: .