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Radius of a cylinder is equal to the side of an equilateral triangle having area 16√3 cm² and height of the cylinder is equal to the perimeter of the triangle. Then find the volume of cylinder.

  • A.1536π cu.cm
  • B.1518π cu.cm
  • C.1620π cu.cm
  • D.1460π cu.cm

Answer: A

Area of equilateral triangle = 16√3 cm²
WKT, Area of equilateral triangle = √3/4 a2
√3/4 a² = 16√3
a² = 64
a = 8 cm

Side of an equilateral triangle = Radius of a cylinder
a = r
r = 8cm
Perimeter of equilateral triangle = 3a = 3(8) = 24 cm

Perimeter of equilateral triangle = Height of cylinder
So, h = 24 cm
Volume of cylinder = πr²h
= π x 8 x 8 x 24
= 1536π cm³.

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