Question

Find the area of a circle whose radius is $14\,cm$.

Answer 1

Hint: Here we need to find the area of a circle and whose radius is $14\,cm$. To find the area of the circle we have a standard formula as $A = \pi {r^2}$. We know the value of $\pi $ and the value of radius $r$ 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 solution:
Circle with radius $r=14cm$ is shown below:

The circle is a two dimensional figure and we have to determine the area, where the area is the region or space occupied by the circular field. To determine the area of a circle we have the 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 centimetres. So, we get the area of the circle using the formula in the unit $c{m^2}$.
To find the area of a circle, we use formula $A = \pi {r^2}$. The radius of the circle is given as $14\,cm$.
By substituting, we get,
$A = \pi {r^2}$
$ \Rightarrow A = \pi {\left( {14\,cm} \right)^2}$
$ \Rightarrow A = \pi {\left( {14} \right)^2}$ $c{m^2}$
We know that a square of fourteen is $196$. Simplifying the calculations, we get,
$ \Rightarrow A = 196\pi $$c{m^2}$
Therefore, the area of a circle with a radius $14\,cm$ is $196\pi $ square centimetres.
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 = 196\left( {\dfrac{{22}}{7}} \right)$ square centimetres
Further simplifying the calculations by cancelling the common factors in numerator and denominator, we have,
$ \Rightarrow A = 28 \times 22$ square centimetres
On further simplification, we have,
$ \Rightarrow A = 616$ square centimetres
Hence the area of a circle whose radius is $14\,cm$ inches is $616$ square centimetres.

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. If we are given the diameter of a circle and asked it area, then we can apply the same formula by finding the radius of circle using $Diameter = \left( {\dfrac{{Radius}}{2}} \right)$.