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

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

1. A

2. B

3. C

$2.5\pi {\mathrm{cm}}^{2}$

4. D

none of these

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Solution:

Let $A$ be the area and 0 (in radians) be the sector angle.  Then,

Let $\mathrm{\Delta }\theta$ be an error in $\theta$ and $\mathrm{\Delta A}$ be the corresponding error in $A.$

Then,

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