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A solid cylinder of radius R cm and height H cm is melted and recast into smaller identical solid cylinders of height h cm and radius r cm. The number of smaller solid cylinders obtained is :

  1. RHrh\dfrac{RH}{rh}

  2. R2Hr2h\dfrac{R^2H}{r^2h}

  3. R2H ÷ r2h2

  4. RH2rh\dfrac{RH^2}{rh}

Mensuration

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Answer

Given,

A solid cylinder of radius R cm and height H cm is melted and recast into smaller identical solid cylinders of height h cm and radius r cm.

Let no. of smaller cylinders formed be n.

∴ Volume of larger cylinder = n × Volume of one smaller cylinder

⇒ πR2H = n × πr2h

⇒ n = πR2Hπr2h=R2Hr2h\dfrac{πR^2H}{πr^2h} = \dfrac{R^2H}{r^2h}

Hence, Option 2 is the correct option.

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