Question

A sector in a pie graph is 12 cm^2, radius is 4cm, what is the angle?

Answer 1

`1.5` (rad) `~~85.94` degrees

Explanation:

Radius of Circle = 4cm

Recall : Area of disk = `pi*r^2`

Here, the area of our graph = `pi*4^2 = 16*pi` cm²

Then our sector of `12` cm² is representing `12/(16*pi)` of the pie graph.
And `12/(16*pi)=3/(4*pi)~~0.2387~~23.87%`
``
``

Therefore, the `12` cm² sector represents exactly `0.75/pi` of the pie graph.
``
(It represents approximately `23.87%` of pie chart.)

Now we want the angle of the sector (in radian measure)
If the sector cover `100%` of the graph, then we have the angle measure is equal to `2pi`

Thus :
`1 <=> 2pi` (rad)
`0.75<=>1.5pi` (rad)
`0.75/pi<=>1.5` (rad)

The angle measure of the sector is equal to `1.5` rad.