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Question
A square tile of length 20 cm has four quarter circles at each corner as shown in the following figure (i). Find the area of shaded portion. Another tile with same dimensions has a circle in the centre of the tile [see figure (ii)]. If the circle touches all 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)
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| (i) | (ii) |
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Solution
(i) Area of shaded portion
= Area of square – 4 × Area of quarter circle
= `20 xx 20 - 4 xx (πr^2)/4` ...[∵ Area of square = (side)2 and area of quarter circle = `1/4` area of a circle]
= `400 - 4 xx 22/7 xx 1/4 xx 10 xx 10` ...[∵ Radius of quarter circle = `1/2` side of square = 10 cm]
= `400 - 2200/7`
= `600/7`
= 85.71 cm2 ≈ 86 cm2
(ii) Area of shaded portion
= Area of square – Area of circle
= `20 xx 20 - 22/7 xx 10 xx 10` ...[∵ Radius of circle = `1/2` side of square = 10 cm]
= `400 - 2200/7`
= `600/7` ≈ 86 cm2
Hence, area in both cases is equal i.e. 86 cm2.
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