Question

The circumference of a circle measures \[22\pi \] units. How do you find the area of the circle?

Answer 1

Hint: To find the area of the circle, we have to find the radius of the circle. Using the circumference of the circle, we can find the radius of the circle by equating it with the given circumference. Using the radius obtained from the circumference we can find the area of the circle, by putting the value of r in the formula for area of the circle.

Complete step-by-step solution:
Circumference of the circle can be defined as the linear length of the circle. It has the formula:
\[C=2\pi r\]
where r is the radius of the circle
Area of the circle can be defined as the space enclosed by the circle. It has the formula:
Area = \[\pi {{r}^{2}}\]
According to the question, we have been given the circumference of the circle. Using the equation of the circumference of the circle we can find out the radius of the circle and then can proceed with the area of the circle.
Circumference = \[22\pi \]
\[2\pi r=22\pi \]
\[\pi \]is removed as it is present on both sides of the equality, we get
\[\Rightarrow 2r=22\]
\[\Rightarrow r=11\]
Now we have with us the radius of the circle, so we can use this to find the area of the circle.
\[Area=\pi {{r}^{2}}\]
Substituting the value of r in the formula of area of the circle,
\[\Rightarrow Area=\pi {{(11)}^{2}}\]
\[\Rightarrow Area=121\pi \]
Therefore, the area of the circle is \[121\pi \].

Note: Circumference and the perimeter of the circle mean the same thing. The given circumference should be equated with the correct formula. The area of the circle should be calculated correctly to get the correct answer.