Question

A circle with radius \pink{10}10start color #ff00af, 10, end color #ff00af has a sector with a central angle of \purple{\dfrac{2}{5}\pi} 5 2 ​ πstart color #9d38bd, start fraction, 2, divided by, 5, end fraction, pi, end color #9d38bd radians . What is the area of the sector? Either enter an exact answer in terms of \piπpi or use 3.143.143, point, 14 for \piπpi and enter your answer as a decimal.

Answer 1

Area of the sector =
`20\pi units^(2)`

Explanation:

Area of a sector =
`(\theta)/(360) * \pi r^(2)`

Given radius r = 10units

`\theta = (2\pi)/(5)`

`\pi = 3.14`

substituting the given values into the equation above;

Area of the sector =
`(2\pi)/(5*360) * \pi *10^(2)`

Area of the sector
`=(100\pi)/(5)`

Area of the sector =
`20\pi units^(2)`