Final answer:
To find the area that is part of the larger circle but not the smaller one, subtract the area of the smaller circle from the area of the larger circle. The correct answer is 51π square inches.
Step-by-step explanation:
To find the area that is part of the larger circle but not the smaller one, we need to subtract the area of the smaller circle from the area of the larger circle.
The area of a circle is given by the formula A = πr², where r is the radius.
So, the area of the larger circle with a radius of 10 inches is A1 = π(10)² = 100π square inches, and the area of the smaller circle with a radius of 7 inches is A2 = π(7)² = 49π square inches.
Therefore, the area that is part of the larger circle but not the smaller one is A1 - A2 = 100π - 49π = 51π square inches. So, the correct answer is C. 51π square inches.