#### 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.

\[x = 28 cm\]

\[ ∆ x = 0 . 01 cm\]

\[x = 2\pi r\]

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

\[ \Rightarrow \frac{dy}{dx} = \frac{x}{2\pi}\]

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

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

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

Is there an error in this question or solution?

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.