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Calculate the number of equilateral triangle that can be produced by melting and recasting a metallic sphere having a radius equal in length to the side of equilateral triangle.  (The equilateral triangle and sphere are having uniform thickness and also there is no loss of material in melting and recasting).

Calculate the number of equilateral triangle that can be produced by melting and recasting a metallic sphere having a radius equal in length to the side of equilateral triangle.  (The equilateral triangle and sphere are having uniform thickness and also there is no loss of material in melting and recasting). Correct Answer 29

Given∶

Side of an equilateral Δ = Radius of sphere

Formula  Used∶

Area of an equilateral triangle = (√3/4) × side2

Area of sphere = 4πr2  

Calculation∶

Let the side of the equilateral triangle be 'a'

Radius of sphere = side of the equilateral triangle = a

Area of sphere = 4πr2 = 4πa2

Area of equilateral triangle = (√3/4) side2 = (√3/4) × a2

Number of equilateral triangles = Area of sphere/ Area of each equilateral Δ= (4πa2)/(√3/4)a2 = 4π/(√3/4) = 16π/√3 = 16 × 3.14/ 1.73 = 29.04 ≈ 29

∴ 29 equilateral triangle can be produced.

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