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A circular park is surrounded by a road $21$ m wide. If the radius of the park is 105 m, then the area of the road in $m 2$ from the following choices is:

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30, 860 m 2

30, 492 m 2

7623 m 2

15246 m 2

answer is D.

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Detailed Solution

It is given that a circular park is surrounded by a road

21

m wide.
The radius of the park is 105 m.
Question Image

Obtain the area of the park.
Area of the park

= π r 2

= π (105) 2

The radius of the outer circle,

R = 105 + 21

= 126

Area of the outer circle

= π R 2

= π (126) 2

Area of the road

=

total area

−

Area of the park

= π (126) 2 − π (105) 2

= 4851 π = 15, 246 m 2

The area is

15, 246 m 2

.
Hence, option 4) is correct.

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