Q3 of 36 Page 253

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


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


More from this chapter

All 36 →
1

A rectangle whose length and breadth are 12 cm and 5 cm respectively is inscribed in a circle. Find the area of the blue coloured region, as shown in the figure 13.19.


Figure 13.19


 2

ABCD, square park, has each side of length 80 m. There is a flower bed at each corner in the form of a sector of radius 7 m, as shown in figure 13.20. Find the area of the remaining part of the park.


Figure 13.20


 4

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


 5

and are two mutually perpendicular radii of a circle of radius 10.5 cm. D and OD = 6 cm. Find the area of blue coloured region shown in figure 13.23.


Figure 13.23