question_answer

A is the centre of circle whose radius is 8 and B is the centre of a circle whose diameter is 8. If these two circles touch externally, then the area of the circle with diameter AB is

A) \[36\,\pi \]

B) \[64\,\pi \]

C) \[144\,\pi \]

D) \[256\,\pi \]

Correct Answer: A

Solution :

[a] From diagram, Length of diameter AB = 8 + 4 = 12 \[\therefore \]Radius of circle of diameter \[AB=\frac{12}{2}=6\] \[\therefore \]Area of circle of diameter \[AB=\pi {{r}^{2}}=\pi \,{{(6)}^{2}}=36\pi \,c{{m}^{2}}\]