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The Circumference of a Circle is Measured as 28 Cm with an Error of 0.01 Cm. the Percentage Error in the Area is - CBSE (Arts) Class 12 - Mathematics

Question

The circumference of a circle is measured as 28 cm with an error of 0.01 cm. The percentage error in the area is

• $\frac{1}{14}$

• 0.01

• $\frac{1}{7}$

• none of these

Solution

$\frac{1}{14}$

Let x be the radius of the circle and y be its circumference.

$x = 28 cm$

$∆ x = 0 . 01 cm$

$x = 2\pi r$

$y = \pi r^2 = \pi \times \frac{x^2}{4 \pi^2} = \frac{x^2}{4\pi}$

$\Rightarrow \frac{dy}{dx} = \frac{x}{2\pi}$

$\Rightarrow \frac{∆ y}{y} = \frac{x}{2\pi y}dx = \frac{2}{x} \times 0 . 01$

$\Rightarrow \frac{∆ y}{y} \times 100 = \frac{2}{x} = \frac{1}{14}$

$\text { Hence, the percentage error in the area is } \frac{1}{14} .$

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Solution The Circumference of a Circle is Measured as 28 Cm with an Error of 0.01 Cm. the Percentage Error in the Area is Concept: Approximations.
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