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Let

  • radius of circular sheet of paper $= R$
  • radius of the cone $=r$
  • height of cone $= H$

Perimeter of base of cone $= 0.9\times 2\pi R$
$\implies 2\pi r  = 0.9*2\pi R$
$\implies r  = 0.9R$

Now, height of cone $H  = \sqrt{R^{2}-r^{2}}$
$\implies H  = r.\sqrt{(R/r)^{2}-1}$
$\implies r/H= \frac{1}{\sqrt{(1/0.9)^{2}-1}}$
$= 2.06$

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