Chapter 11, Problem 6SAP

To determine

To find: the correct option for the given condition.

Answer to Problem 6SAP

The option A is correct.

Explanation of Solution

Given information:

The condition is given as “If the circumference of a circle is $\frac{2\pi }{3}$ , then what is half of its area”.

Consider the condition.

As the circumference of a circle is $\frac{2\pi }{3}$ and the formula for circumference of a circle is $2\pi r$ .

So,

  $\begin{array}{c}2\pi r=\frac{2\pi }{3}\\ r=\frac{1}{3}\end{array}$

The half of the area of a circle is,

  $\begin{array}{c}\frac{\pi r^2}{2}=\frac{\pi }{2}{\left(\frac{1}{3}\right)}^2\\ =\frac{\pi }{2}\left(\frac{1}{9}\right)\\ =\frac{\pi }{18}\end{array}$

Therefore, the option A is correct.