Q4 of 36 Page 253

ABCD is a square plate of 1 m length. As shown in figure circles are drawn with their center at A, B, C, D respectively, each with radius equal to 42 cm. The blue coloured part at each corner, as shown in the C figure 13.22 is cut. What is the area of the remaining portion of the plate?


Figure 13.22


Side of square plate (a) = 1 m = 100cm


radius of the segment (r) = 42 cm


we can notice that all the sectors can form a circle of radius 42 cm


the area of the remaining portion of the plate =


Area of square plate - area of the circle


= a2 - π r2


= 1002 - π × 422


= 4,458.23 cm2


=0.4458 m2


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Figure 13.20


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Figure 13.21


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Figure 13.23


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