Question

The error in the measurement of radius of a sphere is 2%. What would be the error
in :
(a) Volume of sphere
(b) Surface area of sphere.​

Answer 1

$\huge\boxed{\mathfrak{\fcolorbox{red}{yellow}{ANSWER}}} </p><p>$

$\huge{\sf{\underline{\underline{\orange{Given:}}}}}$

★ error in measurement of radius = 2%

i.e.

${\sf{ \frac{∆r}{r} \times 100 \: = \: 2\%}}$

$\huge{\sf{\underline{\underline{\orange{to \: find:}}}}}$

(a)error in volume of sphere

(b)error in surface area of sphere

$\huge{\sf{\underline{\underline{\orange{solution:}}}}}$

${\boxed{\tt★{\red{Volume \: of \: sphere \: = \: \frac{4}{3} \pi {r}^{3} }}}}$

${\bf{ \frac{∆V}{V} × 100= \: 3 \times \frac{∆r}{r} \times 100}} \\ \\ {\bf{\frac{∆V}{V} × 100= \: 3 \times 2}} \\ \\ {\bf{\frac{∆V}{V} = \: \frac{6}{100}}} \\ \\{\boxed{\bf{\blue{ \frac{∆V}{V} = 0.06}}}}$

________________________

${\boxed{\tt★{\red{S.A. \: of \: sphere \: = \: {4}\pi {r}^{2} }}}}$

${\bf{ \frac{∆A}{A} × 100= \: 2 \times \frac{∆r}{r} \times 100}} \\ \\ {\bf{\frac{∆A}{A} × 100= \: 2 \times 2}} \\ \\ {\bf{\frac{∆A}{A} = \: \frac{4}{100}}} \\ \\{\boxed{\bf{\blue{ \frac{∆A}{A} = 0.04}}}}$

$\large{\boxed{\mathcal{\fcolorbox{red}{pink}{Thank\:my\:answer\:if\:its\:helps}}}}$