Question : A circular park whose diameter is 210 m has a 5 m wide path running around it (on the outside). What is the area (in m²) of the path?
Option 1: 1020$\pi$
Option 2: 1075$\pi$
Option 3: 1050$\pi$
Option 4: 1100$\pi$
Correct Answer: 1075$\pi$
Solution :
According to the question,
Inner radius of the park(r) = $\frac{\text{210 m}}{2}$ = 105 m
Outer radius of the park (R) = 105 m + 5 m = 110 m
Area of circular path
= ${π(R ^{2} − r^{2}})$
= ${π((110)^{2} - (105)^{2})}$
= $π((12100) - (11025))$
= $1075π$
Hence, the correct answer is $1075π$.
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