We have that because the central angle is 90°, the sector represents 1/4 of a circle with a radius of 10 yd.
So, length of the safety rail is given by:
[tex]l=\frac{1}{4}\cdot2\pi r[/tex]
Where:
r = 10 yd
pi = 3.14
Substitute, we have:
[tex]l=\frac{1}{4}\cdot2(3.14)(10)=\frac{1}{4}\cdot62.8=15.7\text{ yd}[/tex]
The Answer is 15.7 yd
Next, area of the deck is given by:
[tex]A=\frac{1}{4}\pi r^2[/tex]
Substitute the values:
[tex]A=\frac{1}{4}(3.14)(10)^2=\frac{1}{4}(3.14)(100)=\frac{314}{4}=78.5\text{ yd}^2[/tex]
The answer is 78.5 yd^2
