Question

A sector has an area of 1/2 π and the central angles of 1/9 π radians. What is the area of the circle?

Answer 1

Answer:

Area of circle is 9π

Step-by-step explanation:

The area of sector of a circle is given by $A=\frac{1}{2}r^2\theta$

Plugging the given values in the formula, we get

$\frac{1}{2}\pi=\frac{1}{2}r^2\cdot\frac{1}{9}\pi$

Cancel out 1/2 and π from both sides, we are left with

$1=r^2\cdot\frac{1}{9}$

Cross multiplying, we get

$r^2=9\\\\r=3$

Therefore, area of circle is given by

$A=\pi r^2\\\\A=\pi(3)^2\\\\A=9\pi$

Area of circle is 9π