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katovenus [111]
3 years ago
9

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

Mathematics
2 answers:
harkovskaia [24]3 years ago
7 0
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

Lemur [1.5K]3 years ago
7 0

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

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