Question

Find the area of the blue sector(s). The diameter of the wheel is 12

Answer 1

We know that to find the area of the entire circle, we are going to use the equation:

$A=\pi r^{2}$

And we know that the diameter is 12. To find the radius, we divide the diameter by 2, so 12/2 = 6. So the radius is 6.

Now we can use this radius in the equation:

$A=\pi (6)^{2}$

$A=36\pi$

Since all of the angles of each section are equal, we can assume that each of the sections has an equal area. There are 5 sections, so we need to divide $36 \pi$ by 5 to find the area of each section:

$\frac{36 \pi}{5} =7.2 \pi$

Each section has an area of $7.2\pi units^{2}$ or, using 3.14 for pi, $7.2*3.14=22.61units^{2}$.

Since we are told to find the area of the blue sections, we know that there are 2 sections that are blue. So we need to multiply the area of each section by 2, to find the area of two of the sections:

$22.61*2=45.22units^{2}$

Therefore, the answer is C) 45.2 $units^{2}$.