Answer :
Given:
GH = 6 cm
XH = 8 cm
To find:
Area of new circle that has diameter GX
Solution:
GX = GH + XH
= 6 cm + 8 cm
GX = 14 cm
Diameter = 14 cm
Radius = 14 ÷ 2 = 7 cm
Area of the circle = πr²
= π × 7²
= π × 49
= 49π cm²
Area of the new circle formed is 49π cm².
The area of a new circle that has line segment GX as its diameter is 49 pi cm squared. Thus option C is the correct option.
Given-
The radius of the small circle g is 6 cm.
The radius of the big circle x is 8 cm.
To get the length of the line segment GX we need to add the line segment HX and GH.
[tex]GX=GH+HX[/tex]
[tex]GX=6+8[/tex]
[tex]GX=14[/tex]
Hence the measure of the length GX is 14 cm.
Now the area of the circle with diameter d can be given as,
[tex]A=\pi \times \dfrac{d^2}{4}[/tex]
In the given problem the area of line segment GX is asked. Thus put the value of GX in the above formula of circle. Therefore,
[tex]A=\pi \times \dfrac{14^2}{4}[/tex]
[tex]A=\pi \times \dfrac{14\times 14}{4}[/tex]
[tex]A=49\pi[/tex]
Hence, the area of a new circle that has line segment GX as its diameter is 49 pi cm squared. Thus option C is the correct option.
For more about the circle, follow the link below-
https://brainly.com/question/11833983