Question

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Given a circle with a central angle of 80° and a radius of 27 cm, determine which of the following statements are true. Select all that apply!

A. The area of the sector is 81 π


B. The area of the circle is 729 π


C. The circumference of the circle is 27 π


D. The arc length of the sector is 12π

Answer 1

`\checkmark \text{B. The area of the circle is } 729\pi,\\\checkmark \text{D. The arc length of the sector is } 12\pi`

Explanation:

Area of a circle with radius
`r`:
`r^2\pi`

Circumference of a sector with radius
`r`:
`2r\pi`

Area of sector with angle
`\theta`:
`r^2\pi\cdot (\theta)/(360)`.

Arc length of sector with angle
`\theta`:
`2r\pi\cdot (\theta)/(360)`

Using these equations, we get the following information:

Area of circle:
`27^2\pi=729\pi`

Circumference of a circle:
`2\cdot 27\cdot \pi=54\pi`

Area of sector:
`27^2\pi\cdot (80)/(360)=162\pi`

Arc length of sector:
`2\cdot 27\cdot \pi \cdot (80)/(360)=12\pi`