help

[dev644]

What is the formula to calculate area and perimeter of major sector of a circle ? And how can we leave the answers in terms of theta,? Radius= 9 and theta= 8 over 3

 

[HallsofIvy]

There are \(\displaystyle 2\pi\) radians in a full circle. A sector of a circle with central angle \(\displaystyle \theta\) is \(\displaystyle \frac{\theta}{2\pi}\) of that circle. A circle with radius r has area \(\displaystyle \pi r^2\) and circumference \(\displaystyle 2\pi r\). So a sector or a circle with radius r with central angle \(\displaystyle \theta\) has area \(\displaystyle \frac{\theta}{2\pi}\left(\pi r^2\right)= \frac{r^2\theta}{2}\) and circumference \(\displaystyle \frac{\theta}{2\pi}\left(2\pi r\right)= \theta r\).

 

[dev644]

So how

There are \(\displaystyle 2\pi\) radians in a full circle. A sector of a circle with central angle \(\displaystyle \theta\) is \(\displaystyle \frac{\theta}{2\pi}\) of that circle. A circle with radius r has area \(\displaystyle \pi r^2\) and circumference \(\displaystyle 2\pi r\). So a sector or a circle with radius r with central angle \(\displaystyle \theta\) has area \(\displaystyle \frac{\theta}{2\pi}\left(\pi r^2\right)= \frac{r^2\theta}{2}\) and circumference \(\displaystyle \frac{\theta}{2\pi}\left(2\pi r\right)= \theta r\).

so how I am gonna apply that to find perimeter and area of major sector leaving answers in terms of theta??

 

[Harry_the_cat]

If the angle in the minor sector is theta, the the angle in the major sector
is 2*pi - theta (and vice versa). The same formulae for perimeter and area are still valid, just the angle is now 2pi - theta.