Question

is the circumference of a circle is equal to the perimeter of a square, what is the ratio of area of the circle to the area of the square

Answer 1

Let the circumference of circle and perimeter of square be x

Then,

$2\pi r=x\\r=\frac{x}{2\pi } =\frac{7x}{44}$

$4s=x\\s=\frac{x}{4}$

Now, $\frac{\pi r^{2} }{s^{2} } = \frac{\frac{22}{7}(\frac{7x}{44} )^{2}}{(\frac{x}{4})^{2} } \\\\\frac{\frac{22}{7}(\frac{49x^{2} }{1936} ) }{\frac{x^{2} }{16} }\\\\\\\frac{\frac{x^{2} }{88} }{\frac{x^{2} }{16} } =\frac{x^{2} }{88}(\frac{16}{x^{2} } )$

Therefore, Required ratio is 16 : 88 or 2 : 11.

Answer 2

Answer:

The ratio of their areas will be √π : 2

Step-by-step explanation:

Let us consider the radius of a circle is 'r'

So the area of a circle is A = π*r²

and the parameter of the circle is 2*π*r

Let the sides of a square b x

So the area of the square is A = x*x = x²

and the parameter of square is 4*x

According to the given condition, the parameter of circle and parameter of the square is equal, so a relation generates;

2*π*r = 4*x

π *r = 2*x

(π *r)/2 = x → (A)

Now taking ratio of their areas,

π*r² : x²

Taking square roots on both sides;

√π*r : x

Substituting the values of equation (A) implies;

√π*r : (π *r)/2

√π : 2

Answer.