#### Question

A round table cover has six equal designs as shown in figure. If the radius of the cover is 28 cm, find the cost of making the designs at the rate of Rs.0.35 per cm^{2}. [Use `sqrt3 = 1.7`]

#### Solution

It can be observed that these designs are segments of the circle.

Consider segment APB. Chord AB is a side of the hexagon. Each chord will substitute 360º/6 = 60º at the centre of the circle.

In ΔOAB,

∠OAB = ∠OBA (As OA = OB)

∠AOB = 60°

∠OAB + ∠OBA + ∠AOB = 180°

2∠OAB = 180° − 60° = 120°

∠OAB = 60°

Therefore, ΔOAB is an equilateral triangle.

Area of ΔOAB = `sqrt3/4 xx ("side")^2`

`=sqrt3/4 xx (28)^2 = 196sqrt3 = 196 xx 1.7 = 333.2 cm^2`

Area of sector OAPB = `60^@/360^@ xx pir^2`

`= 1/6xx 22/7xx28xx28`

`= 1232/3 cm^2`

Area of segment APB = Area of sector OAPB − Area of ΔOAB

`=(1232/3 - 333.2) cm^2`

Therefore are of designs = `6xx(1232/3 - 333.2) cm^2`

`= (2464 - 1999.2)cm^2`

= 464.8 cm^{2}

Cost of making 1 cm^{2} designs = Rs 0.35

Cost of making 464.76 cm^{2} designs = 464.8 x 0.35 = Rs 162.68

Therefore, the cost of making such designs is Rs 162.68.