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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, OB =O'C =35 m
and AB =CD =14 m
Also, AD =FG =120 m
Now, OA =O'D =(35+14) =49 m

Area of the region (boundary) = Area of rectangle ABCD + Area of rectangle EFGH +2 {area of semi-circle with centre O and 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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