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

Area of the sector = 5.73 feet²

Explanation:

An arc length is 3 feet is cut off by a central angle of
`(\pi )/(4)`

We have to find the area of the sector formed.

Area of the sector formed =
`(1)/(2)r^(2)\theta`

If the arc length = 3 feet

Central angle =
`(\pi )/(4)`

Since arc length =
`r\theta`

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

r =
`(3)/((\pi )/(4))=((3)(4))/(\pi )=(12)/(\pi )`

Now area of the sector =
`(1)/(2)((12)/(\pi ))^(2)(\pi )/(4)`

=
`(1)/(2)((144)/(\pi ^(2)))((\pi )/(4))`

=
`(144)/(\pi ^(2))((\pi )/(8))`

=
`(18)/(\pi )`

=
`(18)/(3.14)=5.73` square feet

Therefore, area of the sector formed is 5.73 feet²