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

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Answer 1 · 2015-07-12T01:20:53

#1.5# (rad) #~~85.94# degrees

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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