Question

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Answer 1

Answer:

C. $\sqrt{\pi}$

Step-by-step explanation:

We have been given that a square region with side x and a circular region with radius r have the same area. We are asked to find that x must be how many times as great as r.

We know that area of a square is square of its each side length, so area of square region with side x would be $x^2$.

We also know that area of circle is $\pi r^2$.

Since we have been given that both areas are same, so we will equate both areas as:

$x^2=\pi r^2$

Let us take positive square root of both sides as:

$\sqrt{x^2}=\sqrt{\pi r^2}$

$x=\sqrt{\pi}\cdot \sqrt{r^2}$

$x=\sqrt{\pi}\cdot r$

Let us divide both sides by r:

$\frac{x}{r}=\frac{\sqrt{\pi}\cdot r}{r}$

$\frac{x}{r}=\sqrt{\pi}$

Therefore, x must be $\sqrt{\pi}$ times greater than r and option C is the correct choice.