A group of engineers is building a parabolic satellite dish whose shape will be formed by rotating the curve y=ax^2 about the y-axis. If the dish is to have a 6-foot diameter and a maximum depth of 2 feet, find the value of a and the surface area (in square feet) of the dish.

Answer 1

the 3-foot radius and 2-foot depth means that

y = 2/9 x^2

The arc length of the parabola is

∫[0,3] √(1+y'^2) dx

Now just rotate that, remembering that the circumference of a circle is 2πr.