Question

The area of a circle is 15400 m. Find its circumference
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Answer 1

${\underline{\underline{\bf{Given:}}}}$

• Area of a circle = 15,400 m.

${\underline{\underline{\bf{Need\:to\:find:}}}}$

• The circumference (perimeter) of the circle.

${\underline{\underline{\bf{Formulae\:to\:be\:used:}}}}$

$\underline{\boxed{\sf{{Area}_{(Circle)}=\pi {r}^{2}\:sq.units}}}$

$\underline{\boxed{\sf{{Perimeter}_{(Circle)}=2\pi r\:units}}}$

${\underline{\underline{\bf{Solution:}}}}$

We've to find the perimeter of the circle. We're given with the measure of area of circle. But the measure of radius is not given. So, first let's find the radius of the circle by substituting the measures in the formula of area of circle. And then, we shall find the perimeter. Let's do it !!

★ Radius of the circle:

By substituting the given measures in the formula,

$\:\:\:\:\:\:\:\:\implies{\sf{Area=\pi {r}^{2}\:\:\:\:\:\:(\pi=\frac{22}{7})}}$

$\:\:\:\:\:\:\:\:\implies{\sf{15400=\frac{22}{7}\times {r}^{2}}}$

$\:\:\:\:\:\:\:\:\implies{\sf{15400\times 7=22\times {r}^{2}}}$

$\:\:\:\:\:\:\:\:\implies{\sf{107800=22\times {r}^{2}}}$

$\:\:\:\:\:\:\:\:\implies{\sf{\frac{107800}{22}={r}^{2}}}$

$\:\:\:\:\:\:\:\:\implies{\sf{4900={r}^{2}}}$

$\:\:\:\:\:\:\:\:\implies{\sf{\sqrt{4900}=r}}$

$\:\:\:\:\:\:\:\:\implies{\underline{\underline{\sf{70=r}}}}$

We've obtained the radius of the circle, so now let's find the circumference.

★ Circumference of the circle:

$\:\:\:\:\:\:\:\:\implies{\sf{P=2\pi r\:units\:\:\:\:\:\:\:(\pi=\frac{22}{7})}}$

$\:\:\:\:\:\:\:\:\implies{\sf{P= 2\times \frac{22}{\cancel{7}}\times \cancel{70}}}$

$\:\:\:\:\:\:\:\:\implies{\sf{P=2\times 22\times 10}}$

$\:\:\:\:\:\:\:\:\implies{\sf{P=44\times 10}}$

$\:\:\:\:\:\:\:\:\implies{\underline{\underline{\sf{\red{Perimeter=440\:m}}}}}$

${\underline{\underline{\bf{Required\:answer:}}}}$

• The circumference of the circle is 440 metres.

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