QQuestionMathematics
QuestionMathematics
Drag and drop an answer to each box to derive the formula for the area of sector CAB .
The formula for the area of circle *A* is **Area** = *π**r**^2 *. **Sector** *CAB* is a fraction of circle *A*. In degrees, the fraction is
\frac{\theta}{90^\circ}
In radians, the fraction is
\frac{\theta}{180^\circ}
Inserting this fraction into the formula for the area of a circle, and then simplifying, results in the formula **Area** = \frac{\theta}{2}r^2.
| **Area** | **Area** | **Area** | **Area** | **Area** |
| --- | --- | --- | --- | --- |
| 180° | 2π* 180°* | 2π* 2π* | 2π* 2π* | 2π* 2π* |
12 months agoReport content
Answer
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Step 1:: Begin by understanding the problem.
We are given a sector of a circle, CAB, and we want to find its area. The sector is a fraction of the entire circle, with the fraction being represented by the angle θ in radians.
Step 2:: Recall the formula for the area of a circle, which is A = \pi r^2, where A is the area and r is the radius of the circle.
Step 3:: To find the area of sector CAB, we need to find the fraction of the circle that it represents.
In radians, this fraction is given by $$\frac{\theta}{2\pi}$$.
Step 4:: Multiply the area of the circle by this fraction to get the area of sector CAB:
A_{sector} = A \times \frac{\theta}{2\pi}
Step 5:: Substitute the formula for the area of a circle into this equation:
A_{sector} = \pi r^2 \times \frac{\theta}{2\pi}
Step 6:: Simplify the equation by canceling out the π terms:
A_{sector} = r^2 \times \frac{\theta}{2}
Final Answer
The formula for the area of sector CAB is A_{sector} = \frac{1}{2} r^2 \theta.
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