(Q6) A round table top has six equal designs as shown in the figure. If the radius of the table top is 14 cm., find the cost of making the designs with paint at the rate of 5 per cm2(use√3 = 1.732)

We know that the radius of circumscribing circle of a regular hexagon is equal to the length of its side

14cmr

Each side of regular hexagon = 14cm

Therefore Area of six design segments = Area of circle - Area of the regular heaxagon

Now area of circle = πr2

=
22
7
 ×14×14 = 616cm2 --------(1)
Area of regular hexagon = 6×
√3
4
 a2
           =6×
√3
4
 ××

           =.2cm2

Hence, area of six designs = 616 - .21

            =.79cm2

Therefore cost of painting the design at the rate of 5 per cm2

= .79×5

=.95