Question

A circular painting is surrounded by a circular frame. The radius of the painting is n − 3 and the radius of the full circle formed by the frame is n + 3. Write a polynomial that represents the area of just the frame itself, not including the space covered by the painting.

(The area of a circle is given by A = πr2, where r represents the radius of the circle.)
12πn + 18
12πn
−12πn
18

Answer 1

12πn

Explanation:

area of painting:

π(n − 3)²

area of full frame:

π(n+3)²

area of only frame:

area of full frame - area of painting

π(n+3)² - π(n − 3)²

`\pi \left(n^2+6n+9\right)-\pi \left(n^2-6n+9\right)`

`\pi n^2+6\pi n+9\pi -\pi n^2+6\pi n-9\pi`

`12\pi n`