The perimeter of a particular square and the circumference

Ответ:

nakeytrag

13.01.2022

Mathematics

Ratio of area of the square to the area of the circle = π/4

Step-by-step explanation:

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

The perimeter of a particular square and the circumference of a particular circle are equal.

Perimeter of square = 4 x a = 4a

Circumference of circle = 2πr

Given that

4a = 2πr

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

We need to find the ratio of the area of the square to the area of the circle.

Area of the square = a²

Area of the circle = πr²

$\texttt{Ratio of area of the square to the area of the circle =}\frac{a^2}{\pi r^2}\\\\\texttt{Ratio of area of the square to the area of the circle =}\frac{\left ( \frac{\pi r}{2}\right )^2}{\pi r^2}\\\\\texttt{Ratio of area of the square to the area of the circle = }\frac{\pi}{4}$

Ratio of area of the square to the area of the circle = π/4

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The perimeter of a particular square and the circumference of a particular circle are equal. what is the ratio of the area of the square to the area of the circle? express your answer as a common fraction in terms of $\pi$.

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