Question

1. the figure below shows 2 tangent circles such that the 10 - centimeter diameter of the smaller circle is equal to the radius of the larger circle. what is the area, in square centimeters, of the shaded region? f. 10 g. 75 h. 5π j. 10π k. 75π

Explanation:

Step1: Find radius of smaller circle

The diameter of the smaller circle is 10 cm, so the radius $r_1$ of the smaller circle is $\frac{10}{2}=5$ cm.

Step2: Find radius of larger circle

The radius of the larger circle $r_2$ is equal to the diameter of the smaller circle, so $r_2 = 10$ cm.

Step3: Calculate area of larger circle

The area formula of a circle is $A=\pi r^{2}$. For the larger circle with $r_2 = 10$ cm, its area $A_2=\pi r_2^{2}=\pi\times10^{2}=100\pi$ square - centimeters.

Step4: Calculate area of smaller circle

For the smaller circle with $r_1 = 5$ cm, its area $A_1=\pi r_1^{2}=\pi\times5^{2}=25\pi$ square - centimeters.

Step5: Calculate area of shaded region

The area of the shaded region $A = A_2 - A_1$. Substitute $A_1 = 25\pi$ and $A_2 = 100\pi$ into the formula, we get $A=100\pi-25\pi = 75\pi$ square - centimeters.

Answer:

K. $75\pi$