Question

a wire is in the form of a circle of radius 14 cm. if it is bent into a square, find the area of the square so formed.

Answer 1

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GIVEN :-

• A wire is in the form of a circle of radius 14 cm. if it is bent into a square.

TO FIND :-

• Area of the square formed.

SOLUTION :-

Perimeter of circle = 2πr

Putting all values :-

➪ $\sf\:\:\:{2 \:\times\:\dfrac{22}{7} \:\times\: 14}$

➪ $\sf\:\:\bigg({\dfrac{2 \:\times\: 22\:\times\: 14}{7}\bigg)}$

➪ $\sf\:\:\bigg({\dfrac{2 \:\times\: 22\:\times\: \cancel{14}}{\cancel{7}}\bigg)}$

➪ $\sf\:\:\:{2 \:\times\:22\:\times\: 2}$

➪ $\sf\:\:\:{44 \:\times\: 2}$

➪ $\:\:\:\boxed{\sf{44 \:\times\: 2}}\:\bigstar$

Perimeter of circle = Peimeter of square because square is maded from same wire.

$\therefore$ $\sf{4 \:\times\: (side) \:= \:88 \:cm}$

$\:\:\:\:$ $\sf{side\: = \:\dfrac{88}{4}}$

$\:\:\:\:$ $\boxed{\sf{side\:=\:22\:cm}}\:\bigstar$

NOW,

Area of square = (side)²

Putting value :-

➪ $\:$(22)²

➪ $\:$22 × 22

➪ $\:$484 cm²

$\underline{\boxed {\bold {\therefore \green {Area\: of \:square \:formed \:= \:484 \:cm^2}}}}\:\red\bigstar$

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Answer 2

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GIVEN :-

A wire is in the form of a circle of radius 14 cm. if it is bent into a square.

TO FIND :-

Area of the square formed.

SOLUTION :-

Perimeter of circle = 2πr

Putting all values :-

➪ $\sf\:\:\:{2 \:\times\:\dfrac{22}{7} \:\times\: 14}$

➪ $\sf\:\:\bigg({\dfrac{2 \:\times\: 22\:\times\: 14}{7}\bigg)}$

➪ $\sf\:\:\bigg({\dfrac{2 \:\times\: 22\:\times\: \cancel{14}}{\cancel{7}}\bigg)}$

➪ $\sf\:\:\:{2 \:\times\:22\:\times\: 2}$

➪ $\sf\:\:\:{44 \:\times\: 2}$

➪ $\:\:\:\boxed{\sf{44 \:\times\: 2}}\:\bigstar$

Perimeter of circle = Peimeter of square because square is maded from same wire.

$\therefore$ $\sf{4 \:\times\: (side) \:= \:88 \:cm}$

$\:\:\:\:$ $\sf{side\: = \:\dfrac{88}{4}}$

$\:\:\:\:$ $\boxed{\sf{side\:=\:22\:cm}}\:\bigstar$

NOW,

Area of square = (side)²

Putting value :-

➪ $\:$(22)²

➪ $\:$22 × 22

➪ $\:$484 cm²

$\underline{\boxed {\bold {\therefore \green {Area\: of \:square \:formed \:= \:484 \:cm^2}}}}\:\red\bigstar$

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