Question

The error in measurement the radius of sphere is 3%. What will be the percentage error in measuring the volume of the sphere

Answer 1

V=volume of the sphere and r=radius of sphere

Answer 2

%ERROR OF VOLUME MEASUREMENT IS 9%.

Given:

• Error% in measuring radius of sphere is 3%.

To find:

% error in measuring volume of sphere?

Calculation:

The general expression for volume of sphere is as follows:

$V = \dfrac{4}{3} \pi {r}^{3}$

• Here V is volume and r is radius.

Now, when there is a small % error (< 6%) in measuring the radius of the sphere, we can say that the %error in measuring volume will be:

$\dfrac{\Delta V}{V} = 3 \times \dfrac{\Delta r}{r}$

$\implies\dfrac{\Delta V}{V} = 3 \times 3\%$

$\implies\dfrac{\Delta V}{V} = 9\%$

So, the % error in calculating volume of sphere will be 9%.