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

`A=256.67ft^2`

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)=(1)/(2) \pi r^2`

`A_(sm)=(1)/(2) 3.14 4^2`

`A_(sm)=25.12ft^2`

`A_(70\textdegree)=(1)/(2)r^2 (70\textdegree)/(360\textdegree)`

`A_(70\textdegree)=(1)/(2)*4^2* (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`