Q119 of 131 Page 226

A square tile of length 20 cm has four quarter circles at each corner as shown in Fig. 9.64(i). Find the area of shaded portion. Another tile with same dimensions has a circle in the centre of the tile [Fig. 9.64 (ii)]. If the circle touches all the four sides of the square tile, find the area of the shaded portion. In which tile, area of shaded portion will be more? (Take π = 3.14)

(i) We know that area of a square = (side)2


and area of a circle = ∏r2


Area of quarter circle = × ∏r2 =


Area of the shaded portion of first tile = Area of square - 4 × Area of one quarter circle


= (20)2 - 4 ×


= 400 - 4 × 3.14 × × 10 × 10


= 400 - 314


= 86 cm2


(ii) In the second tile, diameter of the circle = Side of the tile = 20 cm


i.e. radius = 10 cm


Area of the shaded portion of second tile = Area of square - Area of circle


= (20)2 – 3.14 × 10 × 10


= 400 - 314


= 86 cm2


Shaded area in both the tiles is same.


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