Question

what is the sum of the areas of circle c and circle d? 7π units² 14π units² 49π units² 98π units² (image: two overlapping circles with centers c and d, segment cd labeled 7 cm)

Explanation:

Step1: Determine the radius of each circle

From the diagram, the distance between centers \( C \) and \( D \) is \( 7 \) cm, which is also the radius of each circle (since the circles appear to have the same radius, and the segment \( CD \) is a radius for each). So, radius \( r = 7 \) cm for both circle \( C \) and circle \( D \).

Step2: Recall the formula for the area of a circle

The area of a circle is given by \( A = \pi r^2 \).

Step3: Calculate the area of one circle

For one circle with \( r = 7 \), the area is \( \pi \times 7^2 = 49\pi \) square units.

Step4: Calculate the sum of the areas of two circles

Since there are two circles (circle \( C \) and circle \( D \)), we add their areas. So, sum \( = 49\pi + 49\pi = 98\pi \) square units.

Answer:

\( 98\pi \) units\(^2\) (corresponding to the option "98π units²")