A round table cover shown in the adjoining figure has six equal designs. If the radius of the cover is 28 cm, find the cost of making the designs at the rate of ₹ 0.50 per cm². [Use √ 3 = 1.73.]

Question

A round table cover shown in the adjoining figure has six equal designs. If the radius of the cover is 28 cm, find the cost of making the designs at the rate of ₹ 0.50 per cm 2 . [Use √ 3 = 1.73.]

Philoid · Accepted Answer

In the given figure, all the six desings covering equal area of the circle, therefore each design will subtend equal angles at the centre which is equal to (360°/6) i.e. 60°.

Also, the six triangles will be equal in area which is obtained by joining vertices of hexagon to the centre.

The triangle obtained will be equilateral because adjacent sides will be equal to the radius i.e. base angles will be equal and angle b/w them is 60° which concludes that other two angles will also be equal to 60° each.

∴ Area of six equilateral Δ = 6 × (√3/4) × (radius)²

= (3√3/2) × (28)²

= 1.5 × 1.73 × 784

= 2034.48 cm²

Area of Circle = π × (radius)² = (22/7) × (28)² = (22/7) × 784

= 22 × 112

= 2464 cm²

Area of the designs = Area of Circle – Area of six equilateral Δ

= (2464 – 2034.48) cm²

= 429.52 cm²

∴ Cost of making designs =Rs. (0.50 × 429.52) = Rs. 214.76

A round table cover shown in the adjoining figure has six equal designs. If the radius of the cover is 28 cm, find the cost of making the designs at the rate of ₹ 0.50 per cm2. [Use √ 3 = 1.73.]

A round table cover shown in the adjoining figure has six equal designs. If the radius of the cover is 28 cm, find the cost of making the designs at the rate of ₹ 0.50 per cm². [Use √ 3 = 1.73.]