Final answer:
The area of the shaded region in the circle is found using the formula for the area of a circle, which is A = πr². Since the radius is equal to the side length of the equilateral triangle, which is 8 inches, the shaded area is 64π square inches.
This correct answer is c)
Step-by-step explanation:
The student has asked: 'In the circle with center O, points A and B are in the circle, and AOB is an equilateral triangle with side lengths of 8 inches. What is the area, in square inches, of the shaded region of the circle?'
Since AOB is an equilateral triangle, all sides are equal, and the sides are also the radii of the circle. This means the radius (r) of the circle is 8 inches. To find the area of the circle (which represents the shaded region), we use the formula: A = πr². Substituting 8 inches in for r:
A = π × (8 inches)²
A = π × 64 square inches
A = 64π square inches
This matches option c) 64π square inches. So, the area of the shaded region of the circle is 64π square inches.
This correct answer is c)