Question

I NEED HELP ASAP!!!

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

wolf?..... u there?

Answer 2

You need to know the area of a circle, which is calculated via PI*R^2, with R being the radius. Your stage has two radii, the outer circle with R=15 and the inner with R=12. Remember that the radius is half the diameter of a circle.

Calculate the area of both circles and substract the area of the inner circle from the outer one. This gives you the total grey area but with the 'wedge' still included.

Now let's remove the area of the wedge. The wedge is only 75 degrees from a total of 360 degrees. That leaves 360-75 = 285 degrees for the stage. Your final solution is therefore 285/360 * total grey area.

Answer 3

wolf just give me the answer

Answer 4

4585.82 ft2

1856.25ft2

1231.61 ft2

4680.11 ft2

Answer 5

@NLCircle which one of those would it be?

Answer 6

Don't have a calculator. You have the method now, so it should be straightforward to punch in the numbers.

Answer 7

i dont get anything just someone give me the answer!!!!!!!!!!!!

Answer 8

http://www.google.com/search?q=2%5E20
google calculator, hope this helps

Answer 9

i have a tn inspire right next to me

Answer 10

then calculate the total area of the grey circle (assuming there wasnt a wedge missing)
and use @NLCircle 's method to calculate the area of the actual seating area (grey) that has got the wedge missing.

"Calculate the area of both circles and substract the area of the inner circle from the outer one. This gives you the total grey area but with the 'wedge' still included."

Area of a circle = pi r^2

"Now let's remove the area of the wedge. The wedge is only 75 degrees from a total of 360 degrees. That leaves 360-75 = 285 degrees for the stage. Your final solution is therefore 285/360 * total grey area."

= answer

Answer 11

If the total area were a complete circle, then area = PI*r²
total area = PI * 45*45
total area = 6,361.725

We have to subtract the stage area
stage area = PI *12*12
stage area = 452.389

We need to subtract the (75° / 360°) portion from the total area
total area = 6,361.725 -(75° / 360°)*6,361.725
total area = 6,361.725 -1,325.359
total area = 5,036.365 - stage area = 452.389
Shaded area = 4,583.976

Still, I think we have subtracted the 75° degree portion of the stage twice.
So we must add that back.

Answer 12

Total Area = 6,361.725
75° Area = -1,325.359
Sub-Total 5,036.366
Stage 285° -358.141
Total shaded Area 4,678.224