Question

The circumference of a circle is equal to \[72\pi \]. Find the radius of this circle.

Answer 1

Hint: The formula to calculate the circumference of the circle is \[2\pi r\], where \[r\] is the radius of the circle.
Apply this formula of the circumference of the circle, and then use the given conditions to find the required value.

Complete step-by-step solution:

It is given that the circumference of a circle is equal to \[72\pi \].

Let us assume that the radius of the given circle is \[r\].

We know that the circumference of the circle or perimeter of the circle is the measurement of the boundary across any two dimensional circular shape including the circle.

We also know that the formula to calculate the circumference of the circle is \[2\pi r\], where \[r\] is the radius of the circle.

From the above formula of the circumference of the circle and the circumference of the given circle, we get

\[2\pi r = 72\pi \]

Dividing the above equation by \[\pi \] on each of the sides, we get

\[
   \Rightarrow \dfrac{{2\pi r}}{\pi } = \dfrac{{72\pi }}{\pi } \\
   \Rightarrow 2r = 72 \\
\]

Dividing the above equation by 2 on each of the sides, we get

\[
   \Rightarrow \dfrac{{2r}}{2} = \dfrac{{72}}{2} \\
   \Rightarrow r = 36 \\
\]

Thus, the radius of the given circle is 36.

Note: In solving these types of questions, you should be familiar with the formula of calculating the circumference of the circle. Some students use the formula of area of the circle instead of the circumference of the circle, which is wrong. Then use the given conditions and values given in the question, and substitute the values in this formula, to find the required value. Also, we are supposed to write the values properly to avoid any miscalculation.