Question

A circle with radius \pink{5}5start color #ff00af, 5, end color #ff00af has a sector with a central angle of \purple{\dfrac{9}{10}\pi} 10 9 ​ πstart color #9d38bd, start fraction, 9, divided by, 10, end fraction, pi, end color #9d38bd radians . What is the area of the sector?

Answer 1

`A \approx 35.34` sq. units.

Explanation:

A sector of a circle is a "part" of a circle.

We are given that the radius of the circle is "5" and the central angle of a sector of the circle is
`(9)/(10)\pi`

We want the area of the sector.

The angle given is in radians, so we need the formula for area of a sector of a circle (in radians), which is:

`A=(1)/(2)r^2 \theta`

Where

r is the radius

`\theta` is the angle in radians

Substituting the known values, we have:

`A=(1)/(2)r^2 \theta\\A=(1)/(2)(5)^2 ((9\pi)/(10))\\A=(1)/(2)(25)((9\pi)/(10))\\A=(225\pi)/(20)\\A=11.25\pi\\A \approx 35.34`

The area approximately is 35.34