Question

what is the sum of the areas of circle c and circle d?
7 cm
c d
7π units²
14π units²
49π units²
98π units²

Explanation:

Step1: Determine the radius of each circle

From the diagram, the distance between centers C and D is 7 cm, and since the circles appear to have the same radius (as CD is a segment that seems to be a radius for each circle, or the radius is 7 cm? Wait, actually, looking at the diagram, the length from C to D is 7 cm, and since each circle's radius should be equal to CD (as the circles intersect and CD is a radius for each), so radius \( r = 7 \) cm for each circle.

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 \( r = 7 \), area \( A_1 = \pi (7)^2 = 49\pi \) units².

Step4: Calculate the sum of the areas of two circles

Since there are two circles (C and D), sum of areas \( A_{total} = A_1 + A_2 = 49\pi + 49\pi = 98\pi \) units².

Answer:

\( 98\pi \) units² (the last option, assuming the last option is \( 98\pi \) units²)