Question

If fan is fully open, what is the approximate area of the fan? Answer choices are attached.

Answer 1

Answer:

Option B. $78.8\ in^2$

Step-by-step explanation:

step 1

Find the area of a circle with radius 8.5 inches

The area of a circle is equal to

$A=\pi r^{2}$

substitute

$A=\pi (8.5)^{2}$

$A=72.25\pi\ in^2$

step 2

Find put the approximate area of the fan

we know that

The area of complete circle subtends a central angle of 360 degrees

so

using proportion

Find the area that correspond a central angle of  125 degrees

$\frac{72.25\pi}{360^o}=\frac{x}{125^o}\\\\x=72.25\pi(125^o)/360^o\\\\x=25.09\pi\ in^2$

assume

$\pi =3.14$

$25.09(3.14)=78.8\ in^2$