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 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

Answer:a=2/25....90.01ft²

Explanation:

y=ax²

2=a(5)²

2=25a

a=2/25

Find a by x=5, y=2

y=2/25x²

∆y/∆x=4/25x

S=2π|x√1+(4/25x)² dx

2π|x√1+16/625x² dx

625/24π[(1+16.25/25)³/²-(1+0)³/²

625/24π[41√41/125-1]

=90.01ft²