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

1 Answer
Jul 12, 2015

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.

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