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.
[Use π =22/7]
What is the area of the seating portion?
A.) 4585.82 ft2
B.) 1856.25ft2
C.) 1231.61 ft2
D.) 4680.11 ft2

Answer 1

First thing to do is to find the area of the circular room (diameter = 90 ft) and the area of the stage (diameter =24 ft) and subtract the two areas to get just the seating area (ignoring the part that is cut-out). Can you do this part?

Answer 2

90-24=66

Answer 3

No. You need to calculate the area of the larger circle \[A _{L}=\pi r^2=\frac{22}{7} 45^2=?\]and the area of the smaller circle\[A _{S}=\pi r^2=\frac{22}{7} 12^2=?\]

Answer 4

im guessing i multiply them

Answer 5

To figure out the shaded area (seating portion) for now I am ignoring the pie slice and just looking at the whole circle. If we calculate A_L (area of the whole circular room) and subtract A_S (area of the circular stage), that will give us the area of the ring between the two.
\[A_L-A_S\]

Answer 6

So AL is 6364.285714 and AS is 452.5714286 wich = 5911.714285

Answer 7

I don't know if I am going about this completely in the best possible way but......
We know that the "pie" slice is a 75 degree wedge. So we have to subtract 75/360 of the area to subtract that area. Does that make sense?

Answer 8

ohhh ok im starting to get it a little

Answer 9

wich is the area?

Answer 10

What do you mean? "wich is the area?"

Answer 11

is the area is 360

Answer 12

Let me think about this for a couple of minutes.

Answer 13

Okay. Sorry this took me a few minutes because I confused myself. What we want to calculate is the area between the two circles minus the "pie slice". You already calculated the area between the two circles to be 5911.71. The "pie slice" is 75/360ths of the total. Or \[\frac{75}{360} (5911.71)=1231.61\]

Answer 14

Finally the seating area total = 5911.71-1231.61=?

Answer 15

ohhhh ok i was suppose to multiply it by that

Answer 16

4680.1

Answer 17

I guess one other way to say it was that the seating area was (360-75)/360 times (the area between the circles). Well. It took a while but I finally got there.

Answer 18

yea lol , thank you for the help

Answer 19

you're welcome.