Answer:

The Surface area of the dish is 62.83 ft²
Explanation:
Given : A parabolic satellite dish whose shape will be formed by rotating the curve
about the y-axis.
The dish has a 10-ft diameter and a maximum depth of 3 ft,
We have to find the value of a and the surface area S of the dish.
Consider the parabolic satellite dish (shown below) formed by rotating the curve
about the y-axis.
Since the diameter is 10 ft
So radius is 5 ft and height is 3 ft.
So the coordinate A is (5, 3)
Also, (5, 3) satisfies the equation

Thus,

Simplify for a , we have,

Thus, the Equation of curve is

Now, we have to find the surface area of this figure formed by rotating the curve
about the y-axis.
Let R = x
Then Surface area is given by

Finding value of x from
we have,

Thus,

Simplify, we have,


We get,

Simplify, We get,
S = 62.8318530718
Thus, The Surface area of the dish is 62.83 ft²