Krishna
0

Step 1: Use the relationship between circumference and radius to find the radius of the circle.

NOTE: Circumference C = 2 \pi r

r = \frac{C}{2*\pi}

Find the radius of the circle

EXAMPLE: r = \frac{C}{2*\pi}​ r = \frac{22}{2*\pi} (since \pi = \frac{22}{7} = 3.14)

r = \frac{7}{2}

Step 2: Calculate the area of the circle.

Total area of the circle = \pi r^2

Step 3: Set up a formula for the sector area

NOTE: A ratio will need to be constructed. Recall that a circle is composed

of 360 degrees. Therefore, the following ratio can be made,

\frac{\theta}{360} = \frac{\text{sector area} (A_C)}{\text{Total area} (A_T)}

where, \theta = Central angle

Step 3: Plug the sector’s central angle measurement into the formula.

Step 4: Plug the given or calculated area measurement into the formula.

EXAMPLE: \frac{26}{360} = \frac{\text{sector area} (A_C)}{\text{46} (A_T)}

Step 5: Solve the area.

EXAMPLE: \frac{\theta}{360}=\frac{Sector\ area\ \left(A_C\right)}{Total\ area\ \left(A_T\right)}

\frac{26}{360} = \frac{\text{sector area} (A_C)}{\text{46} (A_T)}

\frac{26}{360} * 46 = \text{Sector area} (A_C)

sector area = 3.32