The area of Marco's new circle is 676 pie [tex]cm^{2}[/tex]. the correct answer is option(d).
The formula [tex]\pi r^{2}[/tex] is used to determine the area of a circle, where r is the radius.
The diagram in the attachment shows two circles, one tiny with a radius of GY=10 cm and the other large with a radius of YX=16 cm.
The length of the line GX, which can be obtained by adding GY + YX, or 10 cm + 16 cm = 26 cm, is the radius GX that Marco wishes to use to form the new circle.
Since GX is 26 cm, Marco's new circle will have a 26-centimeter radius.
area of this new circle = [tex]\pi r^{2}[/tex],
where r = radius = 26cm
Hence,
Area = π × [tex]26^{2}[/tex]
[tex]26^{2}[/tex] = 26 × 26 = 676
Area = [tex]\pi[/tex] × 676
Area = 676[tex]\pi[/tex]
Area of new circle= 676 pie [tex]cm^{2}[/tex]
The complete question is:
Point G is the center of the small circle. Point X is the center of the large circle. Points G, Y, and X are all on line segment . as a Marco wants to create a new circle using radius. What will be the area of Marco's new circle?
it lacks the diagram illustrating the circle and the options. The diagram has been attached. These are the options:
a. 10 pie cm2
b. 16 pie cm2
c. 356 pie cm2
d. 676 pie cm2
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