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

Answer:

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

Step-by-step 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 $\theta$:  $r^2\pi\cdot \frac{\theta}{360}$.

Arc length of sector with angle $\theta$: $2r\pi\cdot \frac{\theta}{360}$

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: $27^2\pi\cdot \frac{80}{360}=162\pi$

Arc length of sector: $2\cdot 27\cdot \pi \cdot \frac{80}{360}=12\pi$