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

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)`