Question

Find the area A of the sector of a circle of radius 90 in formed by central angle 1/6 radian.

Answer 1

2121
`in^(2)` Rounded to the nearest inch.

Explanation:

A =
`\pi r^(2)` Is the formula for a circle, but we only have a portion of a circle so we will have to adjust the formula for a part of the circle.

A =
`((\pi )/(6) )/(2\pi )`
`\pi r^(2)` The
`(\pi )/(6)` is the part of the circle and the whole circle is 2
`\pi`

`((\pi )/(6) )/(2\pi )` is the same as
`(\pi )/(6)`÷
`(2\pi )/(1)` Which is the same as
`(\pi )/(6)` x
`(1)/(2\pi )` Which is the same a
`(1)/(12)`

A =
`(1)/(12)`
`\pi`
`90^(2)`

A =
`(1)/(12)`(3.14)(90)(90) = 2119.5. When you use the
`\pi` on your calculator you get a slightly different number. This is due to rounding.

A = 2120.575041