Question

what is the sum of the areas of circle c and circle 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 they intersect symmetrically), the radius \( r \) of each circle is 7 cm.

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 a circle with radius \( r = 7 \) cm, the area \( A_1 = \pi (7)^2 = 49\pi \) square units.

Step4: Calculate the sum of the areas of two circles

Since there are two circles (C and D) with the same area, the sum \( A_{\text{total}} = 2 \times 49\pi = 98\pi \) square units.

Answer:

\( 98\pi \) units\(^2\) (corresponding to the option: \( 98\pi \) units\(^2\))