Question

What is the area of the circle, if the diameter is \[18\]?

Answer 1

Hint: Diameter is the longest chord of a circle and it is twice the length of the radius of the circle. As we all know, the formula to find the area of the circle is \[\pi {{r}^{2}}\]. We can find out the value of the radius from the formula \[r=\dfrac{d}{2}\]. After finding the value of \[r\], we can substitute and calculate the area of the circle.

Complete step by step solution:
Now let us calculate the area of the circle whose diameter is \[18\].

Firstly, let us find out the value of the radius.
\[d=18\]
As mentioned in the hint,
\[\begin{align}
  & r=\dfrac{d}{2} \\
 & \Rightarrow r=\dfrac{18}{2} \\
 & \therefore r=9 \\
\end{align}\]
\[\therefore \]The value of radius is \[9\].
Now let us calculate the area of the circle whose radius is \[9\]
Area of circle= \[\pi {{r}^{2}}\]
Take the value of \[\pi \] as \[3.14\].
\[\begin{align}
  & \Rightarrow 3.14\times 9\times 9 \\
 & =254.34 \\
\end{align}\]
\[\therefore \] The area of the circle whose diameter is 18 is \[254.34\].

Note: The area of a circle can be calculated in another method when diameter is given i.e. the formula would be \[A=\dfrac{1}{4}\pi {{d}^{2}}\].
Let us solve this by using the formula \[A=\dfrac{1}{4}\pi {{d}^{2}}\]
\[\begin{align}
  & \Rightarrow \dfrac{1}{4}\times 3.14\times 18\times 18 \\
 & =\dfrac{1017.36}{4} \\
 & =254.34 \\
\end{align}\]
Since we can observe that both of our solutions are equal, we can follow any one of the methods in calculating the area of the circle when the diameter is given.