A road which is $7\text{ m}$ wide surrounds a circular park whose circumference is $352\text{ m}$. Find the area of the road.
Step-by-Step Solution
Key Concept: $2(22/7) r = 352 \Rightarrow r = 56\text{ m}$. Outer radius $R = 56 + 7 = 63\text{ m}$. Road area $= \pi(R^2 - r^2) = \dfrac{22}{7}(63^2 - 56^2) = \dfrac{22}{7}(119 \times 7) = 22 \times 119 = 2618\text{ m}^2$.
Inner radius $r = 56\text{ m} \Rightarrow R = 63\text{ m}$. [1.0 Mark]
Road Area $= \dfrac{22}{7}(63 - 56)(63 + 56) = 22 \times 119 = 2618\text{ m}^2$. [1.0 Mark]
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🎯 Official CBSE Marking Scheme:
Finding $r = 56\text{ m}, R = 63\text{ m}$: 1.0 Mark
Calculating road area $= 2618\text{ m}^2$: 1.0 Mark
Correct Answer: