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 m^{2}? (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) = 90^{o}

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

Area of part – 1

The area of the sector BAPC =

= × 12^{2} × 90

= 113.04 cm^{2}

Area of square = a^{2}

= 12^{2}

= 144 cm^{2}

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

= 144 – 113.04

= 30.96 cm^{2}

∵ The shapes are identical

The area of part 2 (AQC) = 30.96 cm^{2}

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

= 30.96 + 30.96

= 61.92 cm^{2}

Cost for covering 1 m^{2} silver foil = 100

Cost for covering 61.92 m^{2} silver foil = 61.92 × 100

= 6192

Rate this question :

A regular hexagon of side 10 cm is cut from a plane circular sheet of radius 10 cm as shown in the figure 13.11. Find the area of the remaining part of the sheet. ( = 1.73) (= 3.14)

Gujarat Board Mathematics

A circle is inscribed in APQR where m∠Q = 90, PQ = 8 cm and QR = 6 cm. Find the area of the blue coloured region shown in figure 13.29. (= 3.14)

Figure 13.29

Gujarat Board Mathematics

Figure 13.27 shows a kite formed by a square PQRS and an isosceles right triangle ARB whose congruent sides are 5 cm long. is an arc of a (R, 42). Find the area of the blue coloured region.

Figure 13.27

Gujarat Board Mathematics

Select a proper option (a), (b), (c) or (d) from given options and write in the box given on the right so that the statement becomes correct:

The area of the largest triangle inscribed in a semi-circle of radius 8 is ……

Gujarat Board Mathematics

On a circular table top of radius 30 cm a design is formed leaving an equilateral triangle inscribed in a circle. Find the area of the design. (π = 3.14)

Gujarat Board MathematicsABCD is a square of side 20 cm. Find the area of blue coloured region formed by the semi-circles drawn on each side as shown in figure 13.26. ( = 3.14)

figure 13.26.

Gujarat Board Mathematics

The length of a side of a square garden ABCD is 70 m. A minor segment of (O, OA) is drawn on each of two opposite sides for developing lawn, as shown in figure 13.25. Find the area of the lawn.

figure 13.25

Gujarat Board Mathematics