Question

What is the area of a circle with a circumference of $8\pi $ inches?

Answer 1

Hint: From the given question we have to find the area of a circle having circumference $8\pi $inches. As we know that the circumference of a circle of radius r is given by, $2\pi r$. We try to find r from the given equation. Then using that r we will get the area of the circle that is $\pi {{r}^{2}}$.

Complete step by step solution:
Given a circle of circumference
$\Rightarrow 8\pi $ inches
We know Circumference of a circle is
$2\pi r$
Where r is the radius of the circle
On substituting the values, we get,
$\Rightarrow 2\pi r=8\pi $
$\Rightarrow 2r=8$
On simplifying we get,
$\Rightarrow r=4$ inches
The radius of the circle is 4 inches.
We know Area of the circle is
$\Rightarrow Area=\pi {{r}^{2}}$
Area of a circle is,
$\Rightarrow Area=\pi {{\left( 4 \right)}^{2}}$
$\Rightarrow Area=16\pi $
On simplifying we get.
$\Rightarrow Area=50.24inc{{h}^{2}}$
Therefore, the area of the circle is $50.24inc{{h}^{2}}$.

Note: The area of the circle is given as $\pi {{r}^{2}}$. We use the value of $\pi $ as $\dfrac{22}{7}$ for simpler results and easier calculations and in decimals the value is 3.14 can also be used for calculations, and also on the other hand, the radius needs to be in the proper unit to get the answer correctly. As we are using inches in this problem, we are going to use inches in the whole solution.