The Grand Canyon Skywalk at Eagle Point is a horseshoe shaped steel frame with a glass floor looking down to the Grand Canyon below. The Skywalk extends 70 feet over the canyon rim and is 10 feet wide. The walkway consists of a semicircle with a straight portion on each side as indicated in the diagram below. How many square feet of glass are needed to cover the Skywalk floor? (Round your final answer to 1 decimal place and any intermediate calculations to 2 decimal places. Be sure to include units.)
Answers
Answer: It will be needed 864 square feet of glass to cover the Skywalk floor.
Step-by-step explanation: The figure below shows the area in question.
Area of a circle is given by
[tex]A=\pi.r^{2}[/tex]
The walkway is a semicircle. Then, area will be:
[tex]A=\frac{\pi.r^{2}}{2}[/tex]
The area that will be covered with glass is the area between the outer and the inner circles. So, area is
[tex]A_{t}=A_{outer}-A_{inner}[/tex]
[tex]A_{t}=\frac{\pi.r_{o}^{2}}{2}- \frac{\pi.r_{i}^{2}}{2}[/tex]
[tex]A_{t}=\frac{\pi}{2}(32.5^{2}-22.5^{2})[/tex]
[tex]A_{t}=\frac{\pi}{2}(550)[/tex]
[tex]A_{t}=[/tex] 864
To cover the Skywalk floor is needed 864[tex]ft^{2}[/tex] of glass.
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