Question : A is the centre of a circle whose radius is 8 units, and B is the centre of a circle whose diameter is 8 units. If these two circles touch externally, then the area of the circle with diameter AB is:
Option 1: $36\pi$ sq. units
Option 2: $64\pi$ sq. units
Option 3: $144\pi$ sq. units
Option 4: $256\pi$ sq. units
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Correct Answer: $36\pi$ sq. units
Solution :
The distance between A and B is the sum of their radii = 8 + 4 = 12 units
The diameter AB of the new circle is 12 units.
The radius of the new circle is 6 units.
The area of a circle,
$= \pi r^2=\pi(6^2)=36\pi$ sq. units
Hence, the correct answer is $36\pi$ sq. units.
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