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

Answer:

$A \approx 35.34$ sq. units.

Step-by-step 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 $\frac{9}{10}\pi$

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:

$A=\frac{1}{2}r^2 \theta$

Where

r is the radius

$\theta$ is the angle in radians

Substituting the known values, we have:

$A=\frac{1}{2}r^2 \theta\\A=\frac{1}{2}(5)^2 (\frac{9\pi}{10})\\A=\frac{1}{2}(25)(\frac{9\pi}{10})\\A=\frac{225\pi}{20}\\A=11.25\pi\\A \approx 35.34$

The area approximately is 35.34