Question

The diameter of a circle is $40$ metres. What is the area of a circle in terms of $\pi $?

Answer 1

Hint: Here in this question we want to find the area of a circle and whose diameter is given to us in the question itself. To find the area we have a standard formula as $A = \pi {r^2}$. We know that the diameter of a circle is equal to two times the radius of the circle. Hence, the length of radius can be found and then we substitute known values and determine the area of a circle using the formula.

Complete step by step answer:
To determine the area of a circle we have the standard formula
$A = \pi {r^2}$
where $r$ represents the radius.
The radius is denoted as ‘$R$’ or ‘$r$’. So, we have the diameter of the circle as $40$ metres.
Now, we know that
$\text{Diameter} = 2 \times \left( \text{Radius} \right)$
So, substituting the value of diameter of the circle, we get,
$40\,m = 2 \times \left( \text{Radius} \right)$
$ \Rightarrow \text{Radius} = 20\,m$
Hence, the length of radius is $20\,m$.

In the given question, we are given the length of the radius in metres. So, we get the area of the circle using the formula in the unit ${m^2}$.
To find the area of a circle, we use formula $A = \pi {r^2}$.
The radius of the circle is given as $20\,m$.
By substituting the known values, we get,
$A = \pi {r^2}$
$ \Rightarrow A = \pi {\left( {20\,m} \right)^2}$
$ \therefore A = 400\pi \,{m^2}$

Therefore, the area of a circle with a diameter as $40$ metres is $400\pi \,{m^2}$ in terms of $\pi $.

Note: 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. 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. We can also find the area by substituting in the value of $\pi $ as $3.14$ to find the answer in decimal representation. So, we get,
$ \Rightarrow A = 400\left( {3.14} \right)\,{m^2}$
$ \therefore A = 1256\,{m^2}$ (approx.)