Respuesta :
Sector area= 0.5 r^2 * theta (in radians)
arc length = r*theta
3=r*(0.7854)
r=3.82
sector area= 0.5 * (3.82)^2 * 0.7854 = 5.73 sq ft
arc length = r*theta
3=r*(0.7854)
r=3.82
sector area= 0.5 * (3.82)^2 * 0.7854 = 5.73 sq ft
Answer:
Area of the sector = 5.73 feet²
Step-by-step explanation:
An arc length is 3 feet is cut off by a central angle of [tex]\frac{\pi }{4}[/tex]
We have to find the area of the sector formed.
Area of the sector formed = [tex]\frac{1}{2}r^{2}\theta[/tex]
If the arc length = 3 feet
Central angle = [tex]\frac{\pi }{4}[/tex]
Since arc length = [tex]r\theta[/tex]
3 = r(\frac{\pi }{4})
r = [tex]\frac{3}{\frac{\pi }{4}}=\frac{(3)(4)}{\pi }=\frac{12}{\pi }[/tex]
Now area of the sector = [tex]\frac{1}{2}(\frac{12}{\pi })^{2}\frac{\pi }{4}[/tex]
= [tex]\frac{1}{2}(\frac{144}{\pi ^{2}})(\frac{\pi }{4})[/tex]
= [tex]\frac{144}{\pi ^{2}}(\frac{\pi }{8})[/tex]
= [tex]\frac{18}{\pi }[/tex]
= [tex]\frac{18}{3.14}=5.73[/tex] square feet
Therefore, area of the sector formed is 5.73 feet²
