Question

An arc length 3 feet is cut off by a central angle of pi/4 radians, find the area of the sector formed

Answer 1

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

Answer 2

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 $\frac{\pi }{4}$

We have to find the area of the sector formed.

Area of the sector formed = $\frac{1}{2}r^{2}\theta$

If the arc length = 3 feet

Central angle = $\frac{\pi }{4}$

Since arc length = $r\theta$

3 = r(\frac{\pi }{4})

r = $\frac{3}{\frac{\pi }{4}}=\frac{(3)(4)}{\pi }=\frac{12}{\pi }$

Now area of the sector = $\frac{1}{2}(\frac{12}{\pi })^{2}\frac{\pi }{4}$

= $\frac{1}{2}(\frac{144}{\pi ^{2}})(\frac{\pi }{4})$

= $\frac{144}{\pi ^{2}}(\frac{\pi }{8})$

= $\frac{18}{\pi }$

= $\frac{18}{3.14}=5.73$ square feet

Therefore, area of the sector formed is 5.73 feet²