Question

circle n has a radius of 8 millimeters(mm). circle m has an area of 144π mm². what is the total area (mm²) of circle n and m?
a. 20π
b. 160π
c. 176π
d. 208π

Explanation:

Step1: Find area of Circle N

The formula for the area of a circle is \( A = \pi r^2 \). For Circle N, \( r = 8 \) mm. So, \( A_N=\pi\times8^2 = 64\pi \) \( \text{mm}^2 \).

Step2: Find total area of Circle N and M

The area of Circle M is \( 144\pi \) \( \text{mm}^2 \). Total area \( A = A_N+A_M = 64\pi + 144\pi = 208\pi \) \( \text{mm}^2 \). Wait, no, wait—wait, maybe I misread. Wait, no, let's check again. Wait, the problem says "circle M has an area of \( 144\pi \) \( \text{mm}^2 \), circle N has radius 8 mm. What is total area of circle N and M?" Wait, no, my calculation for Circle N: \( r = 8 \), so \( \pi r^2=\pi\times64 = 64\pi \). Then total area is \( 64\pi + 144\pi = 208\pi \)? But wait, the options: d is \( 208\pi \). Wait, but let me check again. Wait, maybe I made a mistake. Wait, no, \( 8^2 = 64 \), so area of N is \( 64\pi \), area of M is \( 144\pi \), sum is \( 64\pi + 144\pi = 208\pi \). So the answer should be d. Wait, but let me check the problem again. Wait, the original problem: "Circle N has a radius of 8 millimeters (mm). Circle M has an area of \( 144\pi \) \( \text{mm}^2 \). What is the total area, \( \text{mm}^2 \), of circle N and M?" So yes, area of N: \( \pi r^2 = \pi\times8^2 = 64\pi \). Then total area: \( 64\pi + 144\pi = 208\pi \). So the answer is d.

Answer:

d. \( 208\pi \)