Question

1. a circle with an area of 49π cm² is inscribed (tightly inside of) a square. find the area of the square.

Explanation:

Step1: Find the radius of the circle

The area formula of a circle is $A = \pi r^{2}$. Given $A = 49\pi$, we have $\pi r^{2}=49\pi$. Divide both sides by $\pi$: $r^{2}=49$, so $r = 7$ cm.

Step2: Determine the side - length of the square

Since the circle is inscribed in the square, the diameter of the circle is equal to the side - length of the square. The diameter $d = 2r$, and $r = 7$ cm, so $d=14$ cm, which is the side - length of the square.

Step3: Calculate the area of the square

The area formula of a square is $A_{s}=s^{2}$, where $s$ is the side - length. Here $s = 14$ cm, so $A_{s}=14^{2}=196$ $cm^{2}$.

Answer:

$196$ $cm^{2}$