Question : The circumference of the two circles is 264 m and 308 m respectively. What is the difference between the area of the larger circle and the smaller circle?
Option 1: 2002 m2
Option 2: 2010 m2
Option 3: 1890 m2
Option 4: 1990 m2
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Correct Answer: 2002 m 2
Solution :
Let the radius of 1st circle be $r_1$.
Circumference of 1st circle = 264
So, $2\pi r_1=264$
⇒ $2\times \frac{22}{7}\times r_1 = 264$
⇒ $r_1=42$
Let the radius of 2nd circle be $r_2$.
Circumference of 2nd circle = 308
So, $2\pi r_2=308$
⇒ $2\times \frac{22}{7}\times r_2 = 308$
⇒ $r_2=49$
Difference in area = $\pi (r_2^2-r_1^2)$
= $\pi (49^2-42^2)$
= $\frac{22}{7}\times (49-42)(49+42)$
= $\frac{22}{7}\times7\times 91$
= $2002$ m
2
Hence, the correct answer is 2002 m
2
.
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