Question

2. The logo shown below was created by splitting a circle into 6 equal sections. Raphael is creating a stage-sized version of this logo where the shaded portions will be covered in fabric.
If the radius of the circle is 12 feet, how much fabric will he need in order to cover the shaded portions?

In the space that is given, tell what formulas you used and show how solved to get your answer.

Let π =3.14

Answer 1

From the shaded diagram, Raphael will need 3 of the 6 equal portions, or exactly 1/2 of the area of the circle. Given a radius of 12 ft, knowing that the area of any given circle is $\pi r^2$, and knowing that the area of the fabric needs to be half of the total area, we can set up the equation for the area of the fabric $A$:

$A= \frac{1}{2}\pi (12)^2$

Simplifying, we find that the area of the fabric is exactly

$\frac{1}{2} \pi (144)= \frac{144}{2} \pi=72\pi$ ft.² Using the approximation of 3.14 for π, we get an area of approximately $72(3.14)=226.08$ ft² of fabric.