Question

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.)

Answer 1

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

$A=\pi.r^{2}$

The walkway is a semicircle. Then, area will be:

$A=\frac{\pi.r^{2}}{2}$

The area that will be covered with glass is the area between the outer and the inner circles. So, area is

$A_{t}=A_{outer}-A_{inner}$

$A_{t}=\frac{\pi.r_{o}^{2}}{2}- \frac{\pi.r_{i}^{2}}{2}$

$A_{t}=\frac{\pi}{2}(32.5^{2}-22.5^{2})$

$A_{t}=\frac{\pi}{2}(550)$

$A_{t}=$ 864

To cover the Skywalk floor is needed 864$ft^{2}$ of glass.