Question

Given the area of a circle is \[64\pi \] How do you find the radius of the circle?

Answer 1

Hint: Given, Area of a circle is \[64\pi \]
We are very well aware of a circle, so in this question, we will use the area of a circle formula to find the radius of the circle. So the formula is
Area of the circle is \[ = \pi {r^2}\], where r is the radius of the circle.
By putting the value of the area which is given in the question we can find the value of the radius of the circle.

Step by step solution:
Formula for finding the area of the circle is
Area of circle is \[ = \pi {r^2}\], where r is the radius of the circle
According to question, Area \[ = \pi {r^2}\], putting these value of area in above equation we get
\[\begin{array}{l}
64\pi = \pi \times {r^2}\\
 \Rightarrow {r^2} = \dfrac{{64\pi }}{\pi }\\
 \Rightarrow {r^2} = 64\\
 \Rightarrow r = \sqrt {64} \\
 \Rightarrow r = + 8, - 8
\end{array}\]
\[r = - 8\] will get rejected because radius cannot be negative.

So, the radius of the circle is \[8\].

Note:
Sometimes, it is asked to find the diameter of a circle. So the value of the diameter of the circle is 2 times the radius of the circle. We can use diameter directly in the formula to find the area of the circle. We must neglect the negative values because neither radius will be negative nor area of a circle. By using a radius of the circle we can also find the perimeter of a circle by using the formula that is perimeter \[of\,circle\, = \,2 \times \pi \times radius\,of\,circle\] and we can also replace radius from its diameter in this given formula.