Question

An aluminium wire is bent in the form of a square encloses an area of 30.25 square if the same wire is bent in the form of circle then its area will be

Answer 1

$\overline{\underline{\boxed{\sf GIVEN \darr}}}$

An aluminium wire is bent in the form of a square encloses an area of 30.25 square cm if the same wire is bent in the form of circle. What is the area of the circle ?

$\overline{\underline{\boxed{\sf SOLUTION \darr}}}$

Given that :

The aluminium wire is bent in the form of square = 30.25 cm²

So, 30.25 can be written as 3025/100

Now, Formula for getting area of the square is :

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \underline{\blue{\boxed{ \purple{\sf Area \: of \: Square = (Side)²}}}}$

So,

To get the measure of each side we will apply this formula

$\sf (Side)² = \frac{3025}{100} cm²$

$\sf Side = \sqrt{\frac{3025}{100} cm² }$

√3025 = 55

√100 = 10

$\sf Side = \frac{55}{10} cm$

So, each side = 5.5 cm

Now,

Formula for getting Perimeter of Square is :

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \underline{\orange{ \boxed{ \sf{ \pink{Perimeter \: of \: Square = 4 × Side}}}}}$

• Perimeter = 4 × Side

• Putting the value of Side we get

• Perimeter = 4 × 5.5 cm

• Perimeter = 22 cm

Hence, the perimeter is 22 cm

It is Given that :

The same wire is bent into the circle

Circumference of the circle = Length of the Aluminium wire

Formula of Circumference of the circle is :

$\: \: \: \: \: \: \: \: \: \: \: \: \: \blue{\underline{ \boxed{ \green{\sf Circumference \: of \: the \: circle = 2πr}}}}$

2πr = 22 cm

The value of π ( read as pi) is 22/7

2 × 22/7 r² = 22 cm

r = 22 cm × 7/44

r = 7/2 cm

Now, using the formula for getting arsa of the circle

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \blue{ \underline{ \boxed{ \orange{\sf Area \: of \: the \: circle = πr²}}}}$

Area = πr²

• Area = 22/7 × (7/2)²

• Area = 22/7 × 49/4

• Area = 77/2 cm²

• Area = 38.5 cm²

∴ Area of the square is 38.5 cm²

Answer 2

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A steel wire, when bent in the form of a square, encloses an area of 121 sq. cm. The same wire is bent in the form of a circle. Find the area of the circle.

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Solution

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Side of the square =

area

=

121

=11 cm

Perimeter of the square = 4×side=44 cm

Therefore, length of the wire = 44 cm

We know,

Circumference of the circle = Length of the wire

Therefore, Circumference of the circle = 44 cm

Let the radius of the circle be r cm.

Then, 2πr=44

2×

7

22

×r=44

r=7 cm

Therefore, area of the circle = πr

2

=

7

22

×49=154 cm

2

.

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