Question

A metal wire when bent in the form of an equilateral triangle of the
largest area, encloses an area of 484^1/3 cm2. If the same wire is bent into
the form of a circle of the largest area, find the area of a circle.​

Answer 1

Answer:

2117.7 cm²

Step-by-step explanation:

Length of wire = L

Side length of equilateral triangle = a

Perimeter of equilateral triangle = 3a

3a = L

a = L/3

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

484^(1/3) = (√3/4)a²

484^(1/3) = (√3/4)(L/3)²

484^(1/3) = (√3/4)L/9

L = [9 × 484^(1/3)] / (√3/4)

Circumference of circle = L

2πr = L

r = L / (2π)

= [(9 × 484^(1/3)) / (√3/4)] / (2π)

= 25.97 cm

Area of circle = πr²

= 3.14 × (25.97 cm)²

= 2117.7 cm²

Answer 2

Answer:

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