What is the area of sector AOB from a circle with center O whose diameter is 24 inches and an angle AOB = π/6, expressed in terms of π?

What is the area of sector AOB from a circle with center O whose diameter is 24 inches and an angle AOB = π/6, expressed in terms of π?

• A. 6π
• B. 12π
• C. 8π
• D. 3π

Answer: (B)

To find the area of sector AOB in a circle, we can use the formula for the area of a sector, which is given by: \[ \text{Area of Sector} = \frac{1}{2} \times r^2 \times \theta \] where \( r \) is the radius of the circle and \( \theta \) is the angle in radians. First, we need to determine the radius of the circle. The diameter of the circle is given as 24 inches, so the radius \( r \) is: \[ r = \frac{24}{2} = 12 \text{ inches} \] The angle AOB is provided as \( \frac{\pi}{6} \) radians. Now, we can substitute the values of \( r \) and \( \theta \) into the sector area formula: \[ \text{Area of Sector} = \frac{1}{2} \times (12)^2 \times \left(\frac{\pi}{6}\right) \] Calculating \( (12)^2 \): \[ (12)^2 = 144 \] Now substituting this back into the formula: \[ \text

To find the area of sector AOB in a circle, we can use the formula for the area of a sector, which is given by:

[

\text{Area of Sector} = \frac{1}{2} \times r^2 \times \theta

]

where ( r ) is the radius of the circle and ( \theta ) is the angle in radians.

First, we need to determine the radius of the circle. The diameter of the circle is given as 24 inches, so the radius ( r ) is:

[

r = \frac{24}{2} = 12 \text{ inches}

]

The angle AOB is provided as ( \frac{\pi}{6} ) radians. Now, we can substitute the values of ( r ) and ( \theta ) into the sector area formula:

[

\text{Area of Sector} = \frac{1}{2} \times (12)^2 \times \left(\frac{\pi}{6}\right)

]

Calculating ( (12)^2 ):

[

(12)^2 = 144

]

Now substituting this back into the formula:

[

\text