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Stadium Problem: The plan for a new football stadium calls for the stands to be in a
Chapter 12, Problem 2(choose chapter or problem)
Stadium Problem: The plan for a new football stadium calls for the stands to be in a region defined by two concentric ellipses (Figure 12-6b). The outer ellipse is to be 240 yd long and 200 yd wide. The inner ellipse is to be 200 yd long and 100 yd wide. A football field of standard dimensions, 120 yd by 160 ft, will be laid out in the center of the inner ellipse.
a. Find particular equations of the two ellipses.
b. Find the eccentricities of the two ellipses.
c. How much clearance will there be between the corner of the field and the inner ellipse in the direction of the end line?
d. The area of an ellipse is \(\pi a b\), where a and b are the major and minor radii, respectively. To the nearest square yard, what is the area of the stands? If each seat takes about 0.8 square yards, what will be the approximate seating capacity of the stadium?
e. Show that the familiar formula for the area of a circle is a special case of the formula for the area of an ellipse.
Questions & Answers
QUESTION:
Stadium Problem: The plan for a new football stadium calls for the stands to be in a region defined by two concentric ellipses (Figure 12-6b). The outer ellipse is to be 240 yd long and 200 yd wide. The inner ellipse is to be 200 yd long and 100 yd wide. A football field of standard dimensions, 120 yd by 160 ft, will be laid out in the center of the inner ellipse.
a. Find particular equations of the two ellipses.
b. Find the eccentricities of the two ellipses.
c. How much clearance will there be between the corner of the field and the inner ellipse in the direction of the end line?
d. The area of an ellipse is \(\pi a b\), where a and b are the major and minor radii, respectively. To the nearest square yard, what is the area of the stands? If each seat takes about 0.8 square yards, what will be the approximate seating capacity of the stadium?
e. Show that the familiar formula for the area of a circle is a special case of the formula for the area of an ellipse.
ANSWER:Step 1 of 6
We are given that
The outer ellipse is to be 240 yards long and 240 yards wide.
The inner ellipse is to be 200 yards long and 100 yards wide.
A football field of standard dimensions, 120 yards by 160 feet, will be laid out in the center of the inner ellipse.