Question : The difference between the areas of two concentric circles is 264 cm2. What is the difference between the square of their radius? (use $\pi=\frac{22}{7}$)
Option 1: 70
Option 2: 140
Option 3: 84
Option 4: 64
Correct Answer: 84
Solution :
Given: The difference between the areas of two concentric circles is 264 cm
2
.
The area of the circle $=\pi R^2$ where $R$ is the radius.
According to the question,
$\pi R^2–\pi r^2=264$
⇒ $\frac{22}{7}\times(R^2–r^2)=264$
⇒ $(R^2–r^2)=\frac{264\times 7}{22}$
⇒ $R^2–r^2=\frac{1848}{22}=84$
Hence, the correct answer is 84.
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