中二數學 - 急!

Diameter of the cylinder = px, where p = pi = 22/7.
Height of the cylinder = 2x/5. Therefore, area of curved surface = (px)(2x/5) which is given as 1000p. Therefore,
px(2x/5) = 1000p
x^2 = 2500
x = 50.
Radius of cylinder = x/2 = 25.
Height = 2x/5 = 100/5 = 20.
Volume = p x (radius)^2 x height = p x 25 x 25 x 20 = 12500(pi).
When we spread out the curved surface, it is a rectangle with height = 2x/5 and length = (pi)x. That is height = 20 and length = 50(pi).
Length of staircase = diagonal of the rectangle = L.
By Pythagoras theorem,
L^2 = [50(pi)]^2 + 20^2
= 2500 x 3.1416 x 3.1416 + 400 = 25074.126
Therefore, length of staircase = sqrt(25074.126) = 158. ( 3 sig. fig.)

2008-08-28 22:14:32 補充：
Correction: In line 1, it should be circumference of cylinder, not diameter.