Question

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If the perimeter of a circle is half to that of a square, then the ratio of the area of the circle to the area of the square is:-
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Answer 1

Answer: 7:22

Step-by-step explanation:

❍ Given :-

• Perimeter of a circle is equal to half of perimeter of square

❍ To Find :-

• Ratio of Area of circle and Square

✏ Formulas to be used :-

• Perimeter of a circle = 2π(radius)
• Perimeter of Square = 4 x side
• Area of a circle = π(radius)²
• Area of a square = (side)²

❍ Solution :-

⇝ Assume that Radius of circle = r

⇝ Side of square = a

Equate the perimeter of circle with half of perimeter of square.

$→ 2\pi r = (\frac{1}{2}) \times 4a$

$\sf → \fbox{a = \pi r}$

➸ Now, find the area of circle and area of square,

• Area of the circle = πr²
• Area of the square = a²

➸ Substitute a = πr in area of the square

Area of the square = (πr)² = π²r²

→ Find ratio of area of circle to area of square

→ πr² : π²r²

→ 1 : π

→ Using π = $\frac{22}{7}$

$→1 : \frac{22}{7}$

$→\fbox{7 : 22}$

Therefore, the answer is 7:22 .

Answer 2

Answer: 7:22

Step-by-step explanation:

❍ Given :-

Perimeter of a circle is equal to half of perimeter of square

❍ To Find :-

Ratio of Area of circle and Square

✏ Formulas to be used :-

Perimeter of a circle = 2π(radius)

Perimeter of Square = 4 x side

Area of a circle = π(radius)²

Area of a square = (side)²

❍ Solution :-

⇝ Assume that Radius of circle = r

⇝ Side of square = a

Equate the perimeter of circle with half of perimeter of square.

→ 2\pi r = (\frac{1}{2}) \times 4a→2πr=(

2

1

)×4a

\sf → \fbox{a = \pi r}→

a = \pir

➸ Now, find the area of circle and area of square,

Area of the circle = πr²

Area of the square = a²

➸ Substitute a = πr in area of the square

Area of the square = (πr)² = π²r²

→ Find ratio of area of circle to area of square

→ πr² : π²r²

→ 1 : π

→ Using π = \frac{22}{7}

7

22

→1 : \frac{22}{7} →1:

7

22

→\fbox{7 : 22}→

7 : 22

Therefore, the answer is 7:22.

hope it helps ♡

#MichAditi✨✌️