AngelQuakes
contestada

Find the area of the sector with a central angle of 60° and a radius of 5 inches. Round to the nearest tenth. A) 5.2 in2 B) 10.5 in2 C) 13.1 in2 D) 26.2 in2

Respuesta :

irspow
Set up a proportional ratio considering that the total area is πr^2 so:

a/(πr^2)=α°/360°

a=(απr^2)/360, since α=60° and r=5

a=(60π5^2)/360 in^2

a≈13.0899...

a≈13.1 in^2  (to nearest tenth of a square inch)

calculista

Answer:

The answer is the option C

[tex]13.1\ in^{2}[/tex]

Step-by-step explanation:

we know that

The area of a circle is equal to

[tex]A=\pi r^{2}[/tex]

In this problem we have

[tex]r=5\ in[/tex]

substitute

[tex]A=\pi (5)^{2}=25\pi\ in^{2}[/tex]

[tex]360\°[/tex] subtends the complete circle of area equal to [tex]25\pi\ in^{2}[/tex]

so by proportion

Find the area of the sector with a central angle of [tex]60\°[/tex]

[tex]\frac{25\pi}{360}\frac{\ in^{2}}{degrees}=\frac{x}{60}\frac{\ in^{2}}{degrees} \\ \\x=25\pi *60/360\\ \\ x= 13.1\ in^{2}[/tex]

Otras preguntas