Question

percentage error in measurement of volume of a sphere is 27% calculate percentage error in measurement of surface area of a sphere​

Answer 1

Answer:

4%

Explanation:

The error in measurement of the radius of a sphere is 2%. We want to determine the error in the calculation of is surface area.

Surface area of a sphere is, A=4πr2.

⇒logA=log4π+2logr.

⇒ddr(logA)=ddr(log4π+2logr).

⇒1AdAdr=2r.

⇒dAA=2drr.

⇒ The error in measurement of the surface area is twice the error in measurement of the radius.

It is given that the error in measurement of the radius of the sphere is 2%.

⇒ The error in measurement of the surface area of the sphere is 4%.