Final answer:
The area part of the larger circle but not the smaller one is found by subtracting the area of the smaller circle from that of the larger circle using the formula A = πr². The calculated area of the annulus is approximately 160.221 square inches, which, when rounded to the nearest whole number, would be 160 square inches, corresponding to an option not listed in the question.
Step-by-step explanation:
To find the area that is part of the larger circle but not the smaller one, we need to calculate the area of the annulus formed by the two circles. We do this by finding the area of each circle separately using the formula for the area of a circle, A = πr², and then subtracting the area of the smaller circle from the area of the larger circle.
The area of the larger circle with a radius of 10 inches is given by:
Alarge = π(10 in)² = π(100 in²) = 314.159 in² (approximately)
The area of the smaller circle with a radius of 7 inches is given by:
Asmall = π(7 in)² = π(49 in²) = 153.938 in² (approximately)
The area that is part of the larger circle but not the smaller one is:
Aannulus = Alarge - Asmall
Aannulus = 314.159 in² - 153.938 in²
Aannulus = 160.221 in² (approximately)
However, none of the provided options exactly matches our calculated value. It appears there may be a calculation or rounding error in the options, and we need to round our result to find the closest match, which is Option D: 160 square inches, when rounding to the nearest whole number (note this option was not in the original list given in the question, so there's an inconsistency).