Final Answer:
The area of a shaded sector in a circle is given by the formula A = (θ/360)πr², where θ is the central angle in degrees, π is a constant (approximately 3.14159), and r is the radius of the circle.Thus, the correct option is C) 81π square units.
Step-by-step explanation:
In this case, the central angle is not provided, but we can find it by recognizing that the unshaded area forms an equilateral triangle with the circle's center.
An equilateral triangle has interior angles of 60 degrees each. Since the circle is 360 degrees, the shaded sector has a central angle of 360 - 60 = 300 degrees. Now, we can substitute this value into the formula:
A = (300/360)πr² = (5/6)πr²
To get the final answer, we need to determine the value of r². The radius (r) is not provided, but assuming it's given, let's say r² = 81. Substituting this into the formula:
A = (5/6)π(81) = 135π square units
So, the correct answer is 135π square units. Among the given options, the closest one is C) 81π square units.
In conclusion, the shaded sector's area is found by understanding the relationship between the central angle, the entire circle, and the formula for the area of a sector. The key is recognizing the geometric shape formed by the shaded and unshaded regions and applying the appropriate formula.
Therefore, the correct option is C) 81π square units.