Question

A circular helicopter landing pad has a radius of 200 feet. Inside the circular pad, red paint covers the outer area evenly, with a width of x feet. White paint covers the inner area

Write a polynomial that represents the area of the circle that is painted white. Write your answers in terms of pie

Answer 1

Answer:

$Area = \pi(40000-400x+x^{2})$

Step-by-step explanation:

Radius of the circular pad = 200 feet

The red paint covers the outer area with a width of x feet and white paint covers the inner area. Since, the width of the area covered by red paint is x feet, the radius of the smaller circle covered with white paint will be 200 - x feet, as shown in the image below.

So,

We have the radius of the circle covered with white paint equal to = r = 200 - x

Area of a circle is calculated as:

$Area=\pi r^{2}$

Using the value of r, we get:

$Area= \pi (200-x)^{2}\\Area = \pi(200-x)^{2}\\Area = \pi(40000-400x+x^{2})$

This polynomial represents the area of the circle that is painted in white.