Question

The figure below shows the top view of a circular room with a circular stage. The diameter of the stage is 24 feet. The shaded portion represents the seating for the audience around the stage. What is the area of the seating portion?

Answer 1

anything?

Answer 2

yeah i got the idea, now i just try to do it as easily (=short) as possible

Answer 3

I know it, dont worry lol

Answer 4

k

Answer 5

:D

Answer 6

anything?

Answer 7

yes yes, im just doing it on paper

Answer 8

ty

Answer 9

did you come up with an answer?

Answer 10

Okay, got it.

First, calculate the areas of the two circles and forget that sector there.

Big circle, 45^2*pi=6361,725124
Small circle,21^2*pi=1385,44236 (we got the 21 from 45-grey area's width,24)

Then, we calculate the areas of the sectors. Now think about the pic as two different circles,


Lets calculate sectors, sector is angle/360*area of full circle

Big circle's sector is 75/360*6361.725124 = 1 325.3594
Small circle's sector is 75/360*1385.44236 = 288.633825

Now lets get the sizes of the shapes we have

Big circle-its sector=5 036.36572 = big shape
Small circle-its sector=1 096.80854 =small shape (stage)


now lets minus from the big grey shape the stage, we get the audience seats area

5036.36572-1096.80854=3 939.55718


Answer: 3 939.55718 ft^2