Question

A fan oscillates 250* and can be felt from a distance of 4 feet away . To the nearest tenth what area of the room can feel the wind from the fan? Use 3.14 for pi .

Answer 1

Answer:

$A=256.67ft^2$

Step-by-step explanation:

From the question we are told that:

Fan oscillates $\theta=250$

Distance $d=>Raduis\ r=4 feet$

Since

 $250\textdegree =180\textdegree +70\textdegree$

Generally the equation for the area A is mathematically given by

 $Area=Area\ of\ semi\ circle\ + area\ of\ 70\textdegree sector$

 $A=A_{sm}+A_{70\textdegree}$

Where

 $A_{sm}=\frac{1}{2} \pi r^2$

 $A_{sm}=\frac{1}{2} 3.14 4^2$

 $A_{sm}=25.12ft^2$

 $A_{70\textdegree}=\frac{1}{2}r^2 \frac{70\textdegree}{360\textdegree}$

 $A_{70\textdegree}=\frac{1}{2}*4^2* \frac{70\textdegree}{360\textdegree}$

 $A_{70\textdegree}=1.55ft^2$

Therefore the area A is given as

 $A=A_{sm}+A_{70\textdegree}$

 $A=25.12ft^2+1.55ft^2$

 $A=256.67ft^2$