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A road which is 7 m wide surrounds a ...

A road which is 7 m wide surrounds a circular park whose circumference is 352 m. Find the area of road.

A

2628 `m^2`

B

2617 `m^2`

C

2618 `m^2`

D

2818 `m^2`

Text Solution

Verified by Experts

The correct Answer is:
C
Let the radius of the park be `rm`
Then , its circumference `=2pirm`
`:.2pir=352implies2xx22/7xxr=352`
`implies r=352xx7/44=56`
Thus, inner radius `=56m`
outer radius `=(56+7)m=63m`
Area of the road `=pi[(63)^(2)-(56)^(2)]m^(2)`
`=22/7xx(63+56)(63-56)m^(2)`
`=(22/7xx119xx7)m^(2)=2618m^(2)`
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