Sector area from radians
We can calculate the area of a sector if we know the:
- radius of the circle
- angle of the sector (in radians)
The equation
A=\frac12\theta r^2
- A is the area of the sector
- \theta is the angle of the sector
- r is the radius of the circle
Finding the angle of the sector
We can rearrange A=\frac12\theta r^2 into:
\theta=\frac{2A}{r^2}
Finding the radius of the circle
We can also rearrange A=\frac12\theta r^2 into:
r=\sqrt{\frac{2A}{\theta}}
| Question | Answer |
|---|
| What is the formula for the area of a sector in radians? | A = \frac12 \theta r^2 |
| What does A represent in the sector area formula? | A is the area of the sector |
| What does \theta represent in the sector area formula? | \theta is the angle of the sector (in radians) |
| What does r represent in the sector area formula? | r is the radius of the circle |
| How do you find the angle \theta of a sector given its area and radius? | \theta = \frac{2A}{r^2} |
| How do you find the radius r of a circle given the sector area and angle? | r = \sqrt{\frac{2A}{\theta}} |
| What two pieces of information are required to calculate the area of a sector? | The radius of the circle and the angle of the sector (in radians) |