Interest in ninth grade mathematics in a school

Solution: (1)① When BC=x, AB=CD= 180? x2，y= 180？ X2x, y=- 12x2+90x,

When x=90, ymax=4050

A: When x=90cm, the maximum value of Y is 4050cm2. ..

② Make BE⊥AD at point E and CE⊥AD at point F through points B and C respectively.

Let BC=x, y=3 16(-x2+360x+32400).

=? 3 16x2+4532x+20253

When x=60, y = 27003 ≈ 4676.5.

A: When x=60cm, the maximum value of Y is 4676.5cm2.

4676.5 > 4050 (8 points)

(2) The correct scheme:

Example solution: when the cross section is semicircular, because 180=πr, its radius is r= 180π, and its area is S= 12π( 180π)2.

≈ 5 156.6 > 4676.5, with a large area.

① Regular octagon and a half, ② Regular decagon and a half, ③ Semicircle, etc.