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?

Question

asked Aug 12, 2020 142k views

1 Answer

Songchenwen · Answer 1 · 2020-08-17T04:30:52+0000

Answer:

Area of circle is 9π

Explanation:

The area of sector of a circle is given by
$A=(1)/(2)r^2\theta$

Plugging the given values in the formula, we get

$(1)/(2)\pi=(1)/(2)r^2\cdot(1)/(9)\pi$

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

$1=r^2\cdot(1)/(9)$

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