Question

A round table top has six equal designs. If the radius of the table top is 14cm. Find the cost

of making the designs with paint at the rate of Rs. 5 per cm2

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Answer 1

Given :

For, A round table top has six equal designs

The radius of the table top = r = 14 cm

The rate of making design = Rs 5 per cm²

To Find :

The Total cost of making

Solution :

Since, The design are equal, then angle made by each design are equal

The angle made by each design sector = 60°

∴ Total angle made by 6 design = 6 × 60° = 360°

The measure of radius from center O = r = 14 cm

Now,

Area of one sector = Area of arc = $\dfrac{\Theta }{360^{\circ}}$ × π × radius²

                                                     = $\dfrac{60^{\circ} }{360^{\circ}}$× 3.14 × (14 cm)²

                                                     = 102.57  cm²

Again

Area of six sector = 6 × Area of one sector

                             = 6 × 102.57 cm²

                             = 615.42 cm²

Now,

∵  The cost of making 1 cm² area = Rs 5

∴  The cost of making 615.42 cm² area = Rs 5 × 615.42

                                                                = Rs 3077.1

Hence, The cost of making design with paints is Rs 3077   Answer