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Q.

Rani bought a new field that is next to one she already owns as shown in the figure below. This field is in the shape of a square of side 70 m. She makes a semi-circular lawn of maximum area in this field. The area of the square field excluding the lawn

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a

1548

m^{2}

b

1228

m^{2}

c

1458

m^{2}

d

1518

m^{2}

Question Image

answer is D.

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Detailed Solution

Given, Rani bought a new field that is next to one she already owns.
Side of square shape field = 70 m.
She makes a semi-circular lawn of maximum area in this field.
We know that, the area of a square is the square of its side and the area of semicircle is

12 π r 2

.
The area of the square field is,

= (50) 2 = 2500 m 2

Again, area of the semi-circular lawn is,

= 227 × 2522 = 68757 = 982.14 m 2

.
Therefore, the area of the remaining land = Area of the whole land – Area of the semicircular lawn

= 2500 − 982 = 1518 m 2

Therefore, the area of the remaining field is 1518

m 2

.
Hence, the correct option is 4.

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