Question

What is the circumference of the circle in terms of $\pi $?

(a) $900\pi $ inches
(b) $90\pi $ inches
(c) \[60\pi \] inches
(d) $30\pi $ inches

Answer 1

Hint: Assume the radius of the circle as r. Now, use the fact that $\pi $ is the ratio of circumference of the circle to the diameter. Assume d as the diameter and use the relation d = 2r to find the relation between the circumference and the radius. Use the formula: \[C=2\pi r\], where ‘C’ is the circumference of the circle, and equate the value of r = 30 inches to calculate the value of C in inches.

Complete step by step answer:
Here, we have been provided with the radius of the circle in the figure shown below and we are asked to find its circumference in terms of $\pi $. First we need to understand the meaning of the symbol $\pi $.

Let us assume the radius the circle as r and its diameter as d. Now, the circumference of a circle is also called its perimeter and it is the length of the boundary of the circle. The symbol $\pi $ is the ratio of the circumference of a circle to its diameter. So, mathematically we have,
$\Rightarrow \pi =\dfrac{C}{d}$
Here C is the circumference of the circle. We know that diameter of a circle is twice its radius mathematically given as d = 2r, so substituting in the above relation we get,
$\Rightarrow \pi =\dfrac{C}{2r}$
On cross multiplication we get,
$\Rightarrow C=2\pi r$
Substituting the given value of r = 30 inches we get,
$\begin{align}
  & \Rightarrow C=2\pi \times 30 \\
 & \therefore C=60\pi \\
\end{align}$
So, the correct answer is “Option c”.

Note: Note that the value of $\pi $ is a constant and in calculation we generally use its value as 3.14 or $\dfrac{22}{7}$. These two values are not exact but they are used for calculation. $\pi $ is an irrational number because it is non – terminating and non – repeating. For all the circles the value of $\pi $ is equal to nearly 3.14 up to two places of decimal and it may differ after that for different circles but that does not matter much.