Question

a circle with the area 100pi has a sector with a central angle of 2/5 pi radians. what is the area of the sector

Answer 1

20 pi of 62.8 square units

Explanation:

`central \: angle \: ( \theta) \\ = (2)/(5) {\pi}^(c) = (2)/(5) * 180 \degree = 72 \degree \\ \\ area \: of \: sector \\ = (\theta)/(360 \degree) * area \: of \: circle \\ \\ = (72 \degree)/(360 \degree) * 100\pi \\ \\ = (1)/(5) * 100\pi \\ \\ \red{ \boxed{ \bold{area \: of \: sector= 20\pi \: {units}^(2) }}} \\ \\ = 20 * 3.14 \\ \\ or \\ \\ \purple{ \boxed{ \bold{area \: of \: sector = 62.8 \: {units}^(2) }}}`