Answer:
To calculate the surface area of the cylinder, we need to find the area of the two circular bases and the lateral surface area.
The formula for the circumference of a circle is:
C = 2πr
where C is the circumference and r is the radius. We can rearrange this formula to solve for the radius:
r = C/2π = 513.88/(2 x 3.14) = 81.91 yards
The formula for the area of a circle is:
A = πr^2
where A is the area and r is the radius. We can use this formula to find the area of one of the circular bases:
B = πr^2 = 3.14 x 81.91^2 = 21,237.93 square yards
The formula for the lateral surface area of a cylinder is:
P x h
where P is the perimeter of the base and h is the height. We can use the formula for the circumference to find the perimeter of the base:
P = C = 513.88 yards
Now we can calculate the lateral surface area:
L = P x h = 513.88 x 11 = 5,652.68 square yards
Finally, we can use the formula for the surface area of a cylinder:
SA = 2B + L = 2(21,237.93) + 5,652.68 = 48,128.54 square yards
Therefore, the surface area of the cylinder is approximately 48,128.54 square yards when rounded to the nearest hundredth.