Question

The radius of cylinder is measured to be $(1.30\pm 0.05)cm$ while its length is measured to be $(3.50\pm 0.10)cm$ then curved surface area of cylinder would be:

• A. $28.6c{m}^2$
• B. $(28.6\pm 0.15)c{m}^2$
• C. $(28.6\pm 2.00)c{m}^2$
• D. $(28.6\pm 0.05)c{m}^2$

Answer 1

The correct option is C $(28.6\pm 2.00)c{m}^2$

$\begin{array}{cc}\text{Given}-& \text{Radius of}\text{Cylinder}=1.30\pm 0.05cm\\ & \text{Length of cylinder}=3.50\pm 0.10cm\end{array}$

$\text{we know curved Surface Area of Cylinder}$

$A=2\pi \cdot r\cdot l-\left(i\right)$

$\begin{array}{cc}\Rightarrow A& =2\pi \cdot \left(1.30\right)\times \left(3.50\right)\\ A& =28.6{cm}^2\end{array}$

$\begin{array}{c}\text{Now calculating error in Ara-}\\ \text{*By error analysis method -}\\ \text{- Take logarithm Both sides in eq(i)}\\ \log A=\log r+\log l+\log \left(2\pi \right)\end{array}$

$\begin{array}{c}\text{Differentiating Both sides -}\\ \frac{dA}{A}=\frac{dr}{r}+\frac{dl}{l}=\frac{0.05}{1.3}+\frac{0.1}{3.5}=0.066\\ \frac{dA}{A}=0.066\end{array}$

$\begin{array}{c}dA=0.066\times A=0.066\times 28.6\\ dA\approx 2.0{cm}^2\\ \text{Area}=28.6\pm 2.00{cm}^2\end{array}$