Question

1. the area of three circular game boards are listed in the table below. complete the chart.

area of game board	length of radius	circumference of game board
9πcm²
πft²

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

Explanation:

Step1: Recall area formula for circle

The area formula of a circle is $A = \pi r^{2}$.

Step2: Find radius for $A = 144\pi$ in²

Given $A=\pi r^{2}=144\pi$, divide both sides by $\pi$: $r^{2}=144$, then $r = 12$ in.

Step3: Find circumference for $r = 12$ in

The circumference formula is $C = 2\pi r$. Substitute $r = 12$ in, so $C=2\pi\times12 = 24\pi$ in.

Step4: Find radius for $A = 9\pi$ cm²

Given $A=\pi r^{2}=9\pi$, divide both sides by $\pi$: $r^{2}=9$, then $r = 3$ cm.

Step5: Find circumference for $r = 3$ cm

Substitute $r = 3$ cm into $C = 2\pi r$, so $C=2\pi\times3=6\pi$ cm.

Step6: Find radius for $A=\pi$ ft²

Given $A=\pi r^{2}=\pi$, divide both sides by $\pi$: $r^{2}=1$, then $r = 1$ ft.

Step7: Find circumference for $r = 1$ ft

Substitute $r = 1$ ft into $C = 2\pi r$, so $C=2\pi\times1 = 2\pi$ ft.

Answer:

Area of game board	Length of radius	Circumference of game board
$9\pi$ cm²	3 cm	$6\pi$ cm
$\pi$ ft²	1 ft	$2\pi$ ft