Question

The radius of the inner circle of a tile pattern shown is x inches. Write a polynomial in standard form to represent the area of the space between the inner and outer circle.

Answer 1

Answer:

Area of a circle:  

$A=\pi r^2$ (where r is the radius)

Area of largest (outer) circle:

$\implies A=\pi (x+6)^2$

Area of inner circle:

$\implies A=\pi x^2$

Area of space between the inner and outer circle:

$\implies \pi (x+6)^2-\pi x^2$

$\implies \pi [(x+6)^2- x^2]$

$\implies \pi (x^2+12x+36- x^2)$

$\implies 12\pi x+36\pi$

Factored:

$\implies 12\pi (x+3)$