a circular marble table top has regular hexagon inscribed in it a coloured marble piece is required to design it - Maths - Areas Related to Circles

Question

a circular marble table top has regular hexagon inscribed in it a
coloured marble piece is required to design it in such a way that
all outer segments are coloured whereas the inner central piece
remains white the radius of the table top is 1meter find the cost
of coloured marble

Manbar Singh · Accepted Answer

Dear Student,

Please find below the solution to the asked query :

Let ABCDEF be a regular hexagon inscribed in a circle with centre at O
Now, ∠AOB = ∠BOC = ∠COD = ∠DOE = ∠EOF = ∠FOA = 3606 = 60°Consider ∆AOB
      OA = OB = 1 m⇒∠OBA = ∠OAB  Angles opposite to equal sides are equalNow, ∠AOB = 60°so, ∠OBA = ∠OAB = 60°  By angle sum propertyarea of ∆AOB = 34OA2 = 1
73 × 14 = 0
4325 m2Area of sector AOB = 60°360°×πOA2 = 16 × 227 × 1 = 0
5238 m2Now, area of coloured design = area of sector AOB - area of ∆AOB = 0
5238 - 0 4325 =  0
0913 m2area of 6 coloured designs = 6 × 0
0913 = 0
5478 m2Cost of making the design = 4000 × 0
5478 = Rs 2191 20

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a circular marble table top has regular hexagon inscribed in it a coloured marble piece is required to design it in such a way that all outer segments are coloured whereas the inner central piece remains white the radius of the table top is 1meter find the cost of coloured marble