point g is the center of the small circle. point x is the center of the large circle. points g, h, and x are…

point g is the center of the small circle. point x is the center of the large circle. points g, h, and x are on line segment gx. what would be the area of a new circle that has line segment gx as its diameter? 16π cm² 36π cm² 49π cm² 98π cm²

point g is the center of the small circle. point x is the center of the large circle. points g, h, and x are on line segment gx. what would be the area of a new circle that has line segment gx as its diameter? 16π cm² 36π cm² 49π cm² 98π cm²

Answer

Answer:

C. $49\pi\ cm^{2}$

Explanation:

Step1: Find the length of GX

The length of GX is the sum of the radius of the small - circle and the radius of the large - circle. The radius of the small circle with center G is $r_1 = 6\ cm$ and the radius of the large circle with center X is $r_2=8\ cm$. So, $GX=6 + 8=14\ cm$.

Step2: Find the radius of the new circle

The new circle has GX as its diameter. Let the radius of the new circle be $r$. Since the diameter $d = GX = 14\ cm$, then $r=\frac{d}{2}=\frac{14}{2}=7\ cm$.

Step3: Calculate the area of the new circle

The area formula of a circle is $A=\pi r^{2}$. Substitute $r = 7\ cm$ into the formula, we get $A=\pi\times(7)^{2}=49\pi\ cm^{2}$.