If the difference bettween the circumference and the radius of a circle is 37 cm , then using $\pi =\frac{22}{7}$ , the circumference$( in\ cm)$ of the circle is:
$( A)\ 154$
$( B)\ 44$
$( C)\ 14$
$( D)\ 7$

Academic Mathematics NCERT Class 10

Given: Difference between the circumference and the radius of a circle $=37\ cm$

To do: To find the circumference$( in\ cm)$ of the circle.

Solution:

Let us say the radius of the given circle is r.

$\therefore$ Perimeter of the circle $=2\pi r$

$=2\times \frac{22}{7} \times r$

Difference between the perimeter and radius of the circle

$=2\times \frac{22}{7} \times r-r$

$=\frac{37}{7} r$

As given, Difference of the perimeter of the circle and its radius is $37\ cm$,

On comparing it, we have,

$\frac{37}{7} r=37$

$\Rightarrow r=7\ cm$

$\therefore $ Perimeter of the given circle $=2\pi r$

$=2\times \frac{22}{7} \times 7$

$=44\ cm$

Thus, The perimeter of the given circle is $44\ cm$.

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Updated on: 10-Oct-2022

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