Question

if the diameter of a circle is equal to the side of a square then the ratio of their areas is

Answer 1

Good Morning!!!

Diameter of a circle having radius R = 2R

Length of sides of a square = =2R

Area of circle ( A ) = π ( R )²

Area of square ( A' ) = 2R × 2R = 4R²

Ratio of their areas are A / A' = π / 4


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Answer 2

Let the diameter and side be x

Area of square = x^2 ...(1)

Radius of circle = diameter /2 = x/2

So, Area of circle = $\pi {r}^{2} = \pi \times {( \frac{x}{2}) }^{2} = \frac{\pi {x}^{2} }{4}$

Ratio of area of square to area of square :

${x}^{2} : \: \frac{\pi {x}^{2} }{4} \\ \\ 1: \frac{\pi}{4} \\ \\ multiply \: the \: whole \: by \: 4 \\ \\ 4:\pi$