Question

The error in the measurement of the radius of a sphere is $0.5\%$. What is the permissible percentage error in the measurement of its surface area?

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

The correct option is A 1

$\begin{array}{c}\text{Surface Area}\left(A\right)=4\pi r^2\\ \text{Taking log}\\ \log A=\log 4\pi +2\log r\end{array}$

$\begin{array}{cc}& \text{Differentiating}\\ & \begin{array}{cc}\frac{\delta A^{}\times 100}{A}=& 2\frac{\delta r}{r}\times 100\\ \frac{\delta r}{r}\times 100& =0.5\%\\ 100\times \frac{\delta A}{A}& =2\times 0.5\\ & =1\%\end{array}\end{array}$