Question

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Find the area of each sector. Show your work.

Answer 1

Answer:

$A_{sector} = \dfrac{100\pi}{3}$

$A_{sector} = 104.7 ~square~units$

Step-by-step explanation:

The area of a full circle is

$A = \pi r^2$

A full circle has a central angle of 360 degrees.

The area of a sector is a fraction of the area of a full circle and is proportional to the central angle of the sector.

For a sector:

$A_{sector} = \dfrac{n}{360^\circ}\pi r^2$

where n = central angle of sector.

Here you have a radius of 10 and a central angle of 120 deg.

$A_{sector} = \dfrac{120^\circ}{360^\circ}\pi(10^2)$

$A_{sector} = \dfrac{1}{3}\pi(10^2)$

$A_{sector} = \dfrac{100\pi}{3} ~square~units$

$A_{sector} = 104.7 ~square~units$