Question: The circumference of two circles is 88 m and 220 m, respectively. What is the difference between the area of the larger circle and the smaller circle?
Options:
A) $ 3422m^{2} $
B) $ 3242m^{2} $
C) $ 3234m^{2} $
D) $ 3424m^{2} $
E) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
- Given, $ 2\pi r _1=88 $
$ \Rightarrow $ $ r _1=\frac{88\times 7}{2\times 22}=14 $
and $ 2\pi r _2=220 $
$ \Rightarrow $ $ r _2=\frac{220\times 7}{2\times 22}=35 $
$ \therefore $ $ \pi (r_2^{2}-r_1^{2})=\frac{22}{7}(35^{2}-14^{2}) $
$ =\frac{22}{7}(1225-196) $
$ =\frac{22}{7}\times 1029=3234 $