Keeping the height same, how many times the radius of the given cylinder should be made to get the cylinder of double the volume of given cylinder?

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Solution

Let the radius and height of the cylinder be r and h.
Volume of the cylinder = $π$ r²h
Let the radius of the new cylinder be R.
It is given that the volume of the new cylinder is twice the volume of the given cylinder.
Thus, we have:
Volume of the new cylinder = 2 × Volume of the given cylinder
$\Rightarrow$ $π$ R²h = 2 × $π$ r²h
$\Rightarrow$ R² = 2 r²
$\Rightarrow$ R = $\sqrt{2}$ r
Hence, the radius of the new cylinder is $\sqrt{2}$ times the radius of the given cylinder.

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