Question

1. two circles have the same center. if their radii are 7 inches and 10 inches, find the area that is part of the larger circle but not the smaller one.

(a) 3 square inches
(b) 17 square inches
(c) 51π square inches
(d) 70π square inches

Explanation:

Step1: Recall area formula for circle

The area formula of a circle is $A = \pi r^{2}$, where $r$ is the radius.

Step2: Calculate area of larger circle

Let $r_1 = 10$ inches. Then $A_1=\pi r_1^{2}=\pi\times(10)^{2}=100\pi$ square - inches.

Step3: Calculate area of smaller circle

Let $r_2 = 7$ inches. Then $A_2=\pi r_2^{2}=\pi\times(7)^{2}=49\pi$ square - inches.

Step4: Find the required area

The area that is part of the larger circle but not the smaller one is $A = A_1 - A_2$. So $A=100\pi-49\pi = 51\pi$ square - inches.

Answer:

C. $51\pi$ square inches