Question

How do you find the area of a circle with diameter 20 inch?

Answer 1

Hint: Diameter of the circle is given. First find out its radius by taking the half of the diameter. Then apply the formula of the area of a circle \[A = \pi {r^2}\]. Substitute the values and put $\pi = \dfrac{{22}}{7}$ to find the final answer.

Complete step-by-step solution:
According to the question, we have been given the diameter of a circle. From this we have to show how we can calculate its area.
We’ll start with finding the radius of the circle from its diameter. We know that the radius of a circle is half of its diameter:
$ \Rightarrow r = \dfrac{d}{2}$
Diameter is given as 20 inch in the question. Putting the value of diameter, we’ll get the radius of the circle:
$ \Rightarrow r = \dfrac{{20}}{2} = 10$
So the radius of the circle is 10 inch.
Now we have to calculate its area. We know that the area of a circle can be obtained by applying the formula as:
\[ \Rightarrow A = \pi {r^2}\]
Putting the value of the radius in this formula, we’ll get:
\[
   \Rightarrow A = \pi {\left( {10} \right)^2} \\
   \Rightarrow A = 100\pi \\
 \]
Further, putting $\pi = \dfrac{{22}}{7}$, we’ll get:
\[
   \Rightarrow A = 100 \times \dfrac{{22}}{7} \\
   \Rightarrow A = 100 \times 3.142 \\
   \Rightarrow A = 314.2 \\
 \]

Thus the area of the circle is \[314.2{\text{ inc}}{{\text{h}}^2}\]

Note: If the radius of the circle is known to us, we can also determine its circumference using the formula as shown below:
$ \Rightarrow C = 2\pi r$
Thus putting the value of radius and taking $\pi = \dfrac{{22}}{7}$, we can easily obtain the circumference of the circle. Circumference is also the perimeter of the circle.