Conic Inequalities: number of seats in elliptical area

[chrozer]

Suppose that you are Chief Mathematician for Readytobuild Construction Company. Your company has a contract to build a football stadium in the form of two concentric ellipses, with the field inside the inner ellipse, and the seats between the two ellipses. The seats are in the intersection of the graphs of x[sup:3u2uekjx]2[/sup:3u2uekjx] + 4y[sup:3u2uekjx]2[/sup:3u2uekjx] ? 100 and 25x[sup:3u2uekjx]2[/sup:3u2uekjx] + 36y[sup:3u2uekjx]2[/sup:3u2uekjx] ? 3600 where each unit of the graph represents 10 meters.

(a) On your own graph paper, draw a graph of the seating area.
(b) From a handbook, you find that the area of an elliptical region is ?ab. The Engineering Department estimates that each seat occupies 0.8 square meter. What is the seating capacity of the stadium?

I graphed this on graphed paper but I don't understand part (b) of the question. How do you solve the question?

 

[stapel]

I don't understand part (b) of the question. How do you solve the question?

They gave you a formula for the area of an ellipse, and asked for the area between the two ellipses. Since this area is the area of the larger ellipse, less the (subtracted out) area of the smaller ellipse, you might want to think about applying the formula they gave you, finding the two areas, and then subtracting. :idea:

Have fun!

Eliz.

 

[chrozer]

Ok so I i found the area of the bigger ellipse which is 120? and the smaller which is 50?. I sbutracted and got the area of the seating area which is 70?. Then i divided it by .8 and got and answer of approx. 274.889? Is that correct?