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 $$r={\displaystyle \frac{d}{2}}$$
By substituting the value of $$d$$,
We get,
$$r={\displaystyle \frac{8}{2}}$$
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,
$$A=\left({\displaystyle \frac{22}{7}}\right)\left(4^2\right)$$
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,
$$A=\left({\displaystyle \frac{22}{7}}\right)(4\times 4)$$
On simplifying,
We get,
$$A={\displaystyle \frac{352}{7}}$$
On further simplifying,
We get,
$$A=50.28$$
Thus we get the area of the circle is $$50.28c{m}^2$$.

Therefore,the area of the circle is $$50.28c{m}^2$$.

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 $$r={\displaystyle \frac{d}{2}}$$ 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 $$A=\pi ({\displaystyle \frac{d}{2}}{)}^2$$ . By substituting the diameter of the circle in this formula, we get the area of the circle. Both will yield the same results.