Question

A group of engineers is building a parabolic satellite dish whose shape will be formed by rotating the curve y=ax2 about the y-axis. If the dish is to have a 8-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

you can find useful formulas here. Pick the one for a paraboloid and use your numbers.

http://www.had2know.com/academics/paraboloid-surface-area-volume-calculator.html

I'm sure you can derive it by calculating the arc length and revolving the curve. The Theorem of Pappus might help.

Answer 2

89.03