Question - Calculate Circumference of Circle from Given Area
Solution:
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:\[ C = 14\sqrt{\pi} \: \text{meters} \]
CamTutor
In regards to math, we are professionals.
Get In Touch
Email: camtutor.ai@gmail.com