Q. 33.8( 4 Votes )

What will be the cost of covering the white portion in figure 13.21 with a silver foil if the rate is Rs. 100 per m2? (π = 3.14)



Figure 13.21

Answer :

Given side of a square (a) = 12 cm


Radius of each sector (r) = 12 cm


since it is square the angle (θ) = 90o


let divide the square into 2 parts. (BAPC, DAQC)


Area of part – 1


The area of the sector BAPC =


= × 122 × 90


= 113.04 cm2


Area of square = a2


= 122


= 144 cm2


Area of part 1 (APC) = Area of square - The area of the sector BAPC


= 144 – 113.04


= 30.96 cm2


The shapes are identical


The area of part 2 (AQC) = 30.96 cm2


Area of the colored region = area of PART 1+ area of part 2


= 30.96 + 30.96


= 61.92 cm2


Cost for covering 1 m2 silver foil = 100


Cost for covering 61.92 m2 silver foil = 61.92 × 100


= 6192


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