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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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