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# Solution for The Circumference of a Circle is Measured as 28 Cm with an Error of 0.01 Cm. the Percentage Error in the Area is (A) 1 14 (B) 0.01 - CBSE (Commerce) 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

(a) $\frac{1}{14}$

(b) 0.01

(c) $\frac{1}{7}$

(d) none of these

#### Solution

(a) $\frac{1}{14}$

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

$x = 28 cm$

$∆ x = 0 . 01 cm$

$x = 2\pi r$

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

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

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

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

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

Is there an error in this question or solution?

#### APPEARS IN

RD Sharma Mathematics for Class 12 by R D Sharma (Set of 2 Volume) (2018-19 Session) (with solutions)
Chapter 14: Differentials, Errors and Approximations
Q: 12 | Page no. 13

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Solution for 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 (A) 1 14 (B) 0.01 concept: Approximations. For the courses CBSE (Commerce), CBSE (Arts), PUC Karnataka Science, CBSE (Science)
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