Question

HELP PLEASE


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.

Two concentric circles are drawn and the area between them is shaded. The diameter of the larger circle is shown as 100 feet. A sector with a central angle of 65 degrees is drawn on the circles. The outer circle is not connected in this sector.

[Use π =22 over 7]

What is the area of the seating portion?

6438.49 ft2

7262.71 ft2

6067.63 ft2

7389.82 ft2

Answer 1

Area of larger circle


A = pi*r^2

A = pi*50^2

A = 2500pi

So the area of the larger circle is 2500pi sq ft

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Area of smaller circle


A = pi*r^2

A = pi*12^2

A = 144pi

So the area of the smaller circle is 144pi sq ft

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Area of the outer ring = Area of larger circle - Area of smaller circle

Area of the outer ring = 2500pi - 144pi

Area of the outer ring = 2356pi

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Now we need the areas of each pie shape (for each circle)


Area of large pie wedge


A = (angle/360)*pi*r^2

A = (65/360)*pi*50^2

A = (8125/18)*pi


Area of small pie wedge


A = (angle/360)*pi*r^2

A = (65/360)*pi*12^2

A = 26pi


So the area of the white region in the outer ring is (8125/18)*pi-26pi = (7657/18)*pi sq ft


Therefore, the area of the shaded region is


2356pi- (7657/18)*pi = (34751/18)*pi


which approximates to 6067.6349 if you use 22/7 for pi

Answer 2

WOW THANK YOU SO MUCH!!! omg ur so amazing!:):)

Answer 3

you're welcome :)