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Question

If a pool has to be constructed with a boundary of width 14 m consisting of two straight sections 120 m long joining semi-circular ends whose inner radius is 35 m. Then, the area of the boundary is


A

7056 m2

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B

7000 m2

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C

7500 m2

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D

7050 m2

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Solution

The correct option is A

7056 m2


We have, OC=OD=35 m
and AC=BD=14 m
Also, AB=CD=FE=GH=120 m
Now, OA=OB=35+14=49 m

Area of the region (boundary) = Area of rectangle ABCD + Area of rectangle EFGH + 2(area of semi-circle with radius 49 m Area of semi-circle with radius 35 m)
=120×14+120×14+2(12×227×49212×227×352)=[1680+1680+227(492352)]=[3360+227(49+35)(4935)]=3360+3696=7056 m2


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