The error in measurement of radius of a sphere is $1 %$ . What is the error in the measurement of volume?

Question

Q. If error in measurement of radius of a sphere is

1 %

, what will be the error in measurement volume?

Answer 1

v o l u m e = \frac{4}{3} π r^{3}

Answer 2

So ,

\frac{Δ V}{V} \times 100 = 3 \times \frac{1}{100} \times 100

Answer 3

∴Percentage error in volume is

3

%

The correct option is B $3 %$ .
$v o l u m e = \frac{4}{3} π r^{3}$
$\frac{Δ V}{V} \times 100 = 3 \times \frac{Δ R}{R} \times 100$
$So ,$ $\frac{Δ V}{V} \times 100 = 3 \times \frac{1}{100} \times 100$
$=3%$
∴Percentage error in volume is $3$ %