Question : A 64 cm wide path is made around a circular garden having a diameter of 10 metres. The area (in m2) of the path is closest to: (Take $\pi=\frac{22}{7}$)
Option 1: 10
Option 2: 21
Option 3: 15
Option 4: 9
Correct Answer: 21
Solution :
Width of the circular path = 64 cm
Diameter of the circular garden = 10m = 1000 cm
The radius of the circular garden = $\frac{1000}{2}$ = 500 cm
Inner radius, $r$ = 500 cm
Outer radius, $R$ = (500 + 64) = 564 cm
Area of path = Outer area – Inner area
= $\pi (R^2-r^2)$
= $\frac{22}{7} \times (564^2 - 500^2)$
= $\frac{22}{7} \times (564 + 500)(564 - 500)$
= $\frac{22}{7} \times 1064 \times 64$
= $214016 $ cm
2
= $21.4016\approx 21$ m
2
Hence, the correct answer is 21.
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