Question

If perimeter of the circle is equal to the perimeter of square then find the ratio of their area

Answer 1

Answer

• $\frac{area \: of \: circle}{area \: of \: square} = \frac{4}{\pi}$

Given:-

• perimeter of circle= perimeter of square

To find:-

• Ratio of area of circle to area of rectangle

Solution:-

Let the radius of circle be r and side of square be a.

$perimeter \: of \: circle = 2\pi \: r$

$perimeter \: of \: square = 4 \times \: a$

Then ATQ,

$2\pi \: r = 4 \: a \\ r = \frac{4a}{2\pi} = \frac{2a}{\pi}$

Now,

$\frac{area \: of \: circle}{area \: of \: square} = \frac{\pi {r}^{2} }{ {a}^{2} }$

Now put the value of r in the above equation,

$= > \frac{area \: of \: circle}{area \: of \: square} = \frac{\pi {r}^{2} }{ {a}^{2} } = \frac{\pi {( \frac{2a}{\pi} )}^{2} }{ {a}^{2} }$

$= > \frac{area \: of \: circle}{area \: of \: square} = \frac{\pi \times 4 {a}^{2} }{ {\pi}^{2} \times {a}^{2} } = \frac{4}{\pi}$

Hence,

$\frac{area \: of \: circle}{area \: of \: square} = \frac{4}{\pi}$

Hope its help uh❤