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?

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:

[

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