Question

A 4% error is made in measuring

the radius of a sphere. Find the
Percentage error in the surface
area.

Answer 1

8.51%

Explanation:

Let us assume the radius of the sphere is r. The surface area of a sphere is:

Surface area = 4πr².

There is a 4% error in the measurement of the radius, therefore the radius being measured = (100% - 4%)r = (96%)r = 0.96r

The surface area as a result of error is:

Surface area after measurement = 4π(0.96r)² = 3.6864πr²

The percentage error is the ratio of the difference between the actual and measured value to the measured value. It is given as:

`Percent\ error =(Actual\ area-Measured\ area)/(Measured \ area)*100\%\\ \\Percent\ error =(4\pi r^2-3.6864\pi r^2)/(3.6864\pi r^2)*100\%\\ \\Percent\ error =(0.3136\pi r^2)/(3.6864\pi r^2)*100\%\\ \\Percent\ error =0.0851*100\%\\\\Percent\ error =8.51\%`