Calculate Circumference of Circle from Given Area
The question in the image asks for the circumference of a circle whose area is 49 m². To find the circumference, we first need to determine the radius of the circle.
The formula for the area of a circle is:
\[ A = \pi r^2 \]
where \( A \) is the area and \( r \) is the radius.
Given that the area \( A \) is 49 m², we can solve for \( r \) as follows:
\[ 49 = \pi r^2 \]
Divide both sides by \( \pi \) to get:
\[ \frac{49}{\pi} = r^2 \]
Take the square root of both sides to solve for \( r \):
\[ r = \sqrt{\frac{49}{\pi}} = \frac{\sqrt{49}}{\sqrt{\pi}} = \frac{7}{\sqrt{\pi}} \]
Now we have the radius. The circumference \( C \) of a circle is given by the formula:
\[ C = 2\pi r \]
We can substitute \( r = \frac{7}{\sqrt{\pi}} \) into this formula to find the circumference:
\[ C = 2\pi\left(\frac{7}{\sqrt{\pi}}\right) \]
Now let's simplify:
\[ C = \frac{14\pi}{\sqrt{\pi}} \]
Multiplying the top and bottom by \( \sqrt{\pi} \) to rationalize the denominator, we get:
\[ C = \frac{14\pi\sqrt{\pi}}{\pi} = 14\sqrt{\pi} \]
Finally, you can leave the answer in terms of \( \pi \) as the question requests. The circumference \( C \) is:
\[ C = 14\sqrt{\pi} \: \text{meters} \]
