The circumference of a circle exceeds the diameter by 16.8 cm. Find the circum­ference of the circle.

Given:

The circumference of a circle exceeds the diameter by 16.8 cm.

To do:

We have to find the circum­ference of the circle.

Solution:

Let the radius of the circle be $r$.

This implies,

Diameter of the circle $=2r$

We know that,

Circumference of a circle of radius $r=2 \pi r$

Therefore,

$2 \times \frac{22}{7} \times r-2r=16.8\ cm$

$44r-14r=7 \times 16.8 \mathrm{~cm}$

$30r=117.6 \mathrm{~cm}$

$r=\frac{117.6}{30} \mathrm{~cm}$

$r=3.92 \mathrm{~cm}$

Circumference of the given circle $=2 \times \frac{22}{7} \times 3.92 \mathrm{cm}$

$=44 \times 0.56 \mathrm{~cm}$

$=24.64 \mathrm{~cm}$

The circumference of the circle is $24.64\ cm$.   

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Updated on: 10-Oct-2022

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