Question

The circumference of a circle is 7π m. what is the area

Answer 1

Answer: 38.4845100065m²

when rounded to the nearest tenth: 38.5m²

when rounded to the nearest hundredth: 38.48m²

when rounded to the nearest thousandth: 38.485m²

Step-by-step explanation:

the formula for finding the area of a circle is $A = \pi r^{2}$, where A = area and r = the radius of the circle.

since you're only given the circumference, we need to calculate the radius of the circle before we can find the area.

• to find the radius of a circle, you can either divide the measure of the diameter by 2 OR use the formula $r=\frac{C}{2\pi}$ where r = radius and C = circumference.
• because there is no given diameter measurement in your question, the best way to find the radius is to use the formula $r=\frac{C}{2\pi}$.

first, plug the given values into the equation.

since $7\pi$ is the given circumference, plug in $7\pi$ for $C$.

• $r=\frac{C}{2\pi}$ ⇒ $r=\frac{7\pi}{2\pi}$

• the equation becomes $r=\frac{7\pi}{2\pi}$, aka radius equals seven times pi divided by two times pi.

now divide $\frac{7\pi}{2\pi}$.

• $\frac{7\pi}{2\pi} = 3.5$

now we know that the radius of the circle is 3.5 :) since we have this information, we can now solve for the area of the circle using the formula $A = \pi r^{2}$.

first, plug in $3.5$ for $r$.

• $A = \pi r^{2}$ ⇒ $A = \pi 3.5^{2}$

now multiply $\pi 3.5^2$, aka pi times three and five tenths squared.

• $\pi 3.5^2 = 38.4845100065$ (if needed, you can round this result to the nearest tenth, hundredth, etc.)

the area of the circle is 38.4845100065m². i hope this helps! have an amazing day <3