Answer:
Step-by-step explanation:
6) We would like to find out the area of the following arcs with ,
- radius = 16 m
- [tex]\theta[/tex] = 75° .
As we know that the area of sector is given by ,
[tex]\longrightarrow Area =\dfrac{\theta}{360^o}\times \pi r^2 [/tex]
Here on substituting the respective values , we have ,
[tex]\longrightarrow Area =\dfrac{75}{360}\times \dfrac{22}{7}\times 16m \times 16m \\[/tex]
Simplify,
[tex]\longrightarrow \underline{\underline{Area =167.61 \ m^2}}[/tex]
8) Again we would like to find out the area with ,
- r = 14ft
- [tex]\theta[/tex] = 19π/12 rad.
Firstly we know that ,
[tex]\longrightarrow \pi \ rad = 180^o[/tex]
So ,
[tex]\longrightarrow 2\pi rad = 360^o [/tex]
Therefore , the formula becomes ,
[tex]\longrightarrow Area =\dfrac{\theta}{2\pi}\times πr^2 [/tex]
Substitute ,
[tex]\longrightarrow Area =\dfrac{19\pi}{12\times 2\pi}\times \pi r^2\\ [/tex]
So that,
[tex]\longrightarrow Area =\dfrac{19}{24}\times \dfrac{22}{7}\times 14ft \times 14ft \\ [/tex]
Simplify,
[tex]\longrightarrow \underline{\underline{ Area = 487.66 ft^2 }}[/tex]
And we are done !
