Question

A wire is bent the form of a squre. This squre enclosed an area of 144m2 . if this wire is bent in the form of a circle,find the area of the circle​

Answer 1

$\huge {\red {\underline {\underline {\mathfrak {Answer}}}}}$

The area of the circle is $\frac{576}{\pi} </strong><strong>m</strong><strong>.</strong><strong>$

$\huge {\red {\underline {\underline {\mathfrak {Explanation}}}}}$

Given,

• Area of square = 144 m^2

Area = (Side)^2

➡ 144 = (Side)^2

➡ Side = √144

➡ Side = 12 m

To find the length of the wire, we need to find the perimeter of square.

Perimeter = 4 × Side

➡ Perimeter = 4 × 12

➡ Perimeter = 48 m

Now, length of wire = 48 m

Since length of wire is equal to circumference of a circle,

•°• Circumference = 2πr

➡ 48 = 2πr

➡ r = 48/2π

➡ r = 24/π m

Now,

Area = πr^2

➡ Area = $\pi \times ( { \frac{24}{\pi}) }^{2}$

➡ Area = $\pi \times \frac{576}{ {\pi}^{2} }$

➡ Area = $\frac{576}{\pi}$

Thus, the area of the circle is $\frac{576}{\pi} \: {m}^{2}$

$\huge {\red {\underline {\underline {\mathfrak {Thank You}}}}}$

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Answer 2

$\underline \mathbb{SOLUTION}$

$\underline \mathbb{GIVEN}$

$= > area \: of \: square = 144 {m}^{2}$

$= > area = {side}^{2}$

$= > side = \sqrt{144}$

$= > side = 12m$

$\underline \mathbb{TO\:FIND}$

》LENGTH OF WIRE

$= > perimeter = 4 \times side$

$\underline \mathbb{ATQ}$

$= > perimeter = 4 \times 12$

$= > perimeter = 48m$

$\underline \mathbb{NOW}$

LENGTH OF WIRE= 48m.

$\underline \mathbb{WE\:KNOW}$

》LENGTH OF WIRE IS EQUAL TO CIRCUMFERENCE OF A CIRCLE,

$circumference = 2\pi \times r$

$= > 48 = 2\pi \times r$

$= > r = \frac{48}{2 \pi}$

$= > r = \frac{24}{\pi }$

$\underline \mathbb{NOW}$

$area = \pi \times {r}^{2}$

$area = \pi \times { \frac{24}{\pi} }^{2}$

$area = \pi \times \frac{576}{ {\pi}^{2} }$

$= > area = \frac{576}{\pi}$

$answer = \frac{576}{\pi} {m}^{2}$

_______________________________________

#BAL

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