Question

The percentage error in the measurement of the volume of a sphere is 6%. What is the percentage in the measurements of surface area

Answer 1

hope it helped
ans is 4%

Answer 2

Answer:

The surface area measurements in Percentage is denoted as 4%

To find:

Percentage in the measurements of surface area  

Solution:

Given : The percentage error in the measurement of the volume of a sphere is 6%.  

We know that

$\text {volume of sphere} = \frac { 4 } { 3 } \pi r ^ { 3 }$

Where (r = radius)

$\begin{array} { c } { \frac { \Delta V } { V } = 6 \% } \\\\ { V = \frac { 4 } { 3 } \pi r ^ { 3 } } \\\\ { \frac { \Delta V } { V } = \frac { \frac { 4 } { 3 } \pi 3 r ^ { 2 } \Delta r } { \frac { 4 } { 3 } \pi r ^ { 3 } } = \frac { 3 \Delta r } { r } } \end{array}$

$\begin{array} { c } { S = 4 \pi r ^ { 2 } } \\\\ { \frac { \Delta S } { S } = \frac { 2 \Delta r } { r } } \\\\ { \therefore \frac { \Delta S } { S } = \frac { 2 } { 3 } \times \frac { \Delta V } { V } } \\\\ { = \frac { 2 } { 3 } \times 6 = 4 \% } \end{array}$

Thus, the surface area measurements in Percentage is denoted as 4%