what is the sum of the areas of circle c and circle d?\n7π units²\n14π units²\n49π units²\n98π units²
what is the sum of the areas of circle c and circle d?\n7π units²\n14π units²\n49π units²\n98π units²
Answer
Answer:
D. $98\pi$ units$^{2}$
Explanation:
Step1: Identify the radius of each circle
The distance between the centers C and D is 7 cm. Since the circles are congruent (symmetric about the line segment CD), the radius $r$ of each circle is 7 cm.
Step2: Recall the area - formula for a circle
The area formula of a circle is $A = \pi r^{2}$, where $r$ is the radius of the circle.
Step3: Calculate the area of one circle
For a circle with $r = 7$ cm, substituting into the formula $A=\pi r^{2}$, we get $A_1=\pi\times(7)^{2}=49\pi$ units$^{2}$.
Step4: Calculate the sum of the areas of two circles
Since we have two congruent circles, the sum of their areas $A_{total}=A_1 + A_2$. And since $A_1 = A_2=49\pi$ units$^{2}$, then $A_{total}=49\pi+49\pi = 98\pi$ units$^{2}$.