Question

the perimeter of a circle is equal to twice of square then the ratio of their areas is​

Answer 1

Given,

The perimeter of a circle is equal to twice the square.

Solution,

Assume that the radius of the circle is $\[r\]$ and the side of the square is $\[a\]$.

Therefore,

$\[\begin{array}{l} \Rightarrow 2 \times \frac{{22}}{7} \times r = 2 \times 4 \times a\\ \Rightarrow \frac{r}{a} = \frac{{2 \times 4 \times 7}}{{2 \times 22}}\\ \Rightarrow \frac{r}{a} = \frac{{14}}{{11}}\end{array}\]$

Now, the ratio of their areas is

$\[\begin{array}{l} \Rightarrow \frac{{\pi {r^2}}}{{{a^2}}}\\ \Rightarrow \pi \times {\left( {\frac{r}{a}} \right)^2}\end{array}\]$

Apply values.

$\[\begin{array}{l} \Rightarrow \frac{{22}}{7} \times {\left( {\frac{{14}}{{11}}} \right)^2}\\ \Rightarrow \frac{{56}}{{11}}\end{array}\]$

Hence, the ratio of their area is $\[\frac{{56}}{{11}}\].$

Answer 2

Ratio of Area of circle and Square is 16:π  or 56:11 if perimeter of a circle is equal to twice of perimeter of square

Given:

• perimeter of a circle is equal to twice 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

Step 1:

Assume that Radius of circle = r

Side of square = a

Step 2:

Equate the perimeter of circle with twice of perimeter of square

2πr=2x4a

=> a = πr/4

Step 3:

Find the  area of circle and area of square

Area of the circle = πr²

Area of the square = a²

Step 4:

Substitute a = πr/4 in area of the square

Area of the square = (πr/4)² = π²r²/16

Step 5:

Find ratio of area of circle to area of square

πr² : π²r²/16

16 : π

or using π = 22/7

16 : 22/7

56 : 11

Ratio of Area of circle and Square is 16:π  or 56:11 if perimeter of a circle is equal to twice of perimeter of square