Find the area of a circle with a circumference of $50$ . $24$ units. $\newline$ $\square$ units $^{2}$

Full solution

Q. Find the area of a circle with a circumference of

50

24

units.

\newline

\square

units

^{2}

Find Radius from Circumference: Use the circumference to find the radius of the circle. $\newline$ The formula for the circumference $C$ of a circle is $C = 2\pi r$ , where $r$ is the radius. $\newline$ We can rearrange this formula to solve for $r$ : $r = \frac{C}{2\pi}$ . $\newline$ Given $C = 50.24$ units, we can calculate $r$ as follows: $\newline$ $r = \frac{50.24}{2\pi}$
Calculate Radius: Calculate the radius. $\newline$ $r = \frac{50.24}{2 \times 3.14159}$ $\newline$ $r \approx \frac{50.24}{6.28318}$ $\newline$ $r \approx 8$ units (rounded to two decimal places for simplicity)
Find Area from Radius: Use the radius to find the area of the circle. $\newline$ The formula for the area $A$ of a circle is $A = \pi r^2$ . $\newline$ Now that we have the radius, we can calculate the area: $\newline$ $A = \pi \times (8)^2$
Calculate Area: Calculate the area. $\newline$ $A = 3.14159 \times 64$ $\newline$ $A \approx 201.06$ units $^2$