Question

What is the area of a circle that has a diameter of 24?

Answer 1

Hint: A circle is the locus of a point moving around a fixed point at a fixed distance from that point. Area of a circle is defined as the region occupied by the circle in a 2-dimensional plane.

The formula for the area of a circle with radius $r$ is given by
$Area=\pi {{r}^{2}}$
Diameter is a line which divides the circle into two equal halves. Mathematically, diameter is twice the radius.
$d=2r$
Now, to calculate the area of a circle with a given diameter, we will first find its radius and then use the above formula to calculate its area.

Complete step by step answer:
Here, diameter of the circle (d) is given as $24$ . since, we know that
$\begin{align}
  & d=2r \\
 & \Rightarrow r=\dfrac{d}{2} \\
 & \Rightarrow r=\dfrac{24}{2} \\
 & \Rightarrow r=12\text{ units} \\
\end{align}$
Now, we have the radius of the circle as 12 units. Using the formula, the area of this circle will be calculated as
$\begin{align}
  & Area=\pi {{r}^{2}} \\
 & \Rightarrow Area=\pi {{\left( 12 \right)}^{2}} \\
 & \Rightarrow Area=144\pi \\
\end{align}$
Using the value of $\pi $ to be $3.14$ , we get
$\begin{align}
  & Area=144\times 3.14 \\
 & \therefore Area=452.74\text{ sq}\text{. units} \\
\end{align}$
Hence, the area of a circle with a diameter 24 units is equal to 452.74 sq. units.

Note: While calculating the area of a circle, always note whether the question contains the value of diameter or radius. If the question contains the value of diameter, either you need to convert it into radius and then use the formula for area of circle or you can also use another formula given by
$Area=\dfrac{\pi {{d}^{2}}}{4}$ .
It’s the same formula as mentioned above, just we have replaced $r$ by $\dfrac{d}{2}$ , where $d$ is the diameter of a circle.