Madison Square Garden in New York City is built in the shape of a circle. Its diameter is 404 feet and it accommodates 20,234 spectators. To the nearest tenth, of a square foot how much area is there for each spectator?
Assuming people are sitting on the ice while the Rangers are losing, ....
area = π(202)^2 ft^2
= 40,804π ft^2
number of square ft per spectator
= 40804π/20234 = appr 6.34 ft^2
To find the area of Madison Square Garden per spectator, we need to calculate the total area of the circle and then divide it by the number of spectators.
Step 1: Calculate the radius of the circle.
The diameter of the circle is given as 404 feet. The radius (r) is half of the diameter, so r = 404/2 = 202 feet.
Step 2: Calculate the area of the circle.
The formula for the area (A) of a circle is A = π * r^2, where π is a mathematical constant approximately equal to 3.14159.
Plugging in the value of the radius, we get A = 3.14159 * (202)^2 = 3.14159 * 40,804 = 127,737.3716 square feet.
Step 3: Divide the total area by the number of spectators.
To find the area per spectator, divide the total area by the number of spectators.
Area per spectator = Total area / Number of spectators
Area per spectator = 127,737.3716 / 20,234
Calculating this value will give us the area per spectator in square feet.