Question

How do you find the area of a circle with a radius of $3$ inches?

Answer 1

Hint: Here in this question we want to find the area of a circle and whose radius is 2 cm. To find the area we have a standard formula is $A = \pi {r^2}$. We know the value of $\pi $ and the value of radius is given to us in the question itself. We substitute known values and determine the area of a circle using the formula.

Complete step by step explanation:
The circle is a two dimensional figure and we have to determine the area, where area is the region or space occupied by the circular field. To determine the area of a circle we have standard formula $A = \pi {r^2}$ where r represents the radius. The radius of a circle is the line segment which joins the centre of the circle to any point on the circle or to the circumference. . The radius is denoted as ‘R’ or ‘r’. The unit for the area is square units. In the given question, we are given the length of the radius in inches. So, we get the area of the circle using the formula in the unit ${\left( {inches} \right)^2}$.
To find the area of a circle, we use formula $A = \pi {r^2}$. The radius of the circle is given as $3$ inches.
By substituting, we get,
$A = \pi {r^2}$
$ \Rightarrow A = \pi {\left( 3 \right)^2}$ square inches
$ \Rightarrow A = 9\pi $square inches
Therefore the area of the circle with a radius $3$ inches is $9\pi $ square inches.
We can substitute the value of $\pi $ to find the area and we can simplify further.
Substituting the value of $\pi $, we have,
$ \Rightarrow A = 9\left( {\dfrac{{22}}{7}} \right)$ square inches
Further simplifying the calculations, we have,
$ \Rightarrow A = \left( {\dfrac{{198}}{7}} \right)$ square inches
On further simplification and representing it in decimal expression, we have,
$ \Rightarrow A = 28.28$ square inches
Hence the area of a circle whose radius is $3$ inches is $28.28$ square inches.

Note: A circle is a closed two dimensional figure. Generally the area is the region occupied by the thing. The area of a circle is defined as the region occupied by the circular region. It can be determined by using formula $A = \pi {r^2}$ where r is the radius of the circle. The radius is denoted by r or R.