Question

If a circle of diameter \[8\] cm. What is the area of the circle ?

Answer 1

Hint:In this question, we need to find the area of the circle. We will use the formula which gives a relation between the area of the circle and the radius of the circle. Given the diameter of the circle is \[8\] cm. We know that radius is the half of the diameter given . From this we can find the radius of the circle. Then by substituting the values of radius \[r\] and \[\pi\] constant in the formula and solve it to get the answer.

Formula used:
Area of the circle,
\[A = \pi r^{2}\]
Where \[A\] is the area of the circle, \[r\] is the radius of the circle and \[\pi\] is a mathematical constant.

Complete step by step answer:
Given, the diameter of the circle, \[d = 8\] cm. We know that the length of radius of the circle is half of the length of the diameter of the circle.
That is \[r = \dfrac{d}{2}\]
By substituting the value of \[d\],
We get,
\[r = \dfrac{8}{2}\]
On simplifying we get,
\[r = 4\]
Thus the radius of the circle is \[4\] cm.

Here we need to find the area of the circle. Let us consider a circle with centre O and radius \[4\] cm,

We will use the area of the circle formula to find the area of the circle.
\[A = \pi r^{2}\]
By substituting, the value of \[r\] and \[\pi\] ,
We get,
\[A = \left( \dfrac{22}{7} \right)\left( 4^{2} \right)\]
We can write \[m^{2} = m \times m\] because we know that the square of the number is the multiple of itself .
Thus we get,
\[A = \left( \dfrac{22}{7} \right)\left( 4 \times 4 \right)\]
On simplifying,
We get,
\[A = \dfrac{352}{7}\]
On further simplifying,
We get,
\[A = 50.28\]
Thus we get the area of the circle is \[50.28\ cm^{2}\].

Therefore,the area of the circle is \[50.28\ cm^{2}\].

Note:The concept used in this problem is the area of the circle. In order to solve this problem ,we need to know the basic formulae for finding the area of a circle . We can also solve this problem by substituting \[r = \dfrac{d}{2}\] in the formula of the area of the circle \[A = \pi r^{2}\] to calculate the area of the circle . By replacing r, we get \[A=\pi (\dfrac{d}{2})^{2}\] . By substituting the diameter of the circle in this formula, we get the area of the circle. Both will yield the same results.