Question

If an error of $1^o$ is made in measuring the angle of a sector of radius $30cm$, then the approximate error in its area is

• A. $450c{m}^2$
• B. $25\pi c{m}^2$
• C. $2.5\pi c{m}^2$
• D. none of these

Answer 1

Answer: (C)

$2.5\pi c{m}^2$

Area of sector $A=\frac{\pi r^2\theta }{360}$

Given $r=30cm,d\theta =1^0$

Approximate error in A is $=dA=\left(\frac{dA}{d\theta }\right)\Delta \theta$

$=\frac{900\pi }{360}$

$\Rightarrow dA=2.5\pi c{m}^2$