Find the circumference of a circle whose area is $301.84\ cm^2$.


Given:

Area of a circle is $301.84\ cm^2$.

To do:

We have to find the circumference of the circle.

Solution:

Let the radius of the circle be $r$.

We know that,

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

Area of a circle of radius $r=\pi r^2$

Therefore,

Area of the given circle $=\frac{22}{7} \times(r)^{2} \mathrm{cm}^{2}$

$301.84=\frac{22}{7} \times r^2 \mathrm{~cm}^{2}$

$r^2=\frac{301.84\times7}{22} \mathrm{~cm}^{2}$

$r^2=96.04 \mathrm{~cm}^{2}$

$r^2=(9.8)^2 \mathrm{~cm}^{2}$

$r=9.8 \mathrm{~cm}$

Circumference of the given circle $=2 \times \frac{22}{7} \times 9.8$

$=61.6 \mathrm{~cm}$

The circumference of the circle is $61.6\ cm$.

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Updated on: 10-Oct-2022

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