Question

A cylindrical vessel having diameter equal to its height is full of water which is poured into two identical cylindrical vessels with diameter 42 cm and height 21 cm which are filled completely. Find the diameter of the cylindrical vessel.

Answer 1

Given: diameter of the cylindrical vessel = height of the vessel 

∴ h = 2r 

Given:

water filled in the cylindrical vessel is poured in two cylindrical vessels 

Volume of a cylindrical vessel = πr² h

So,

volume = πr²(2r) = 2 πr³ 

Volume of vessel with diameter 42 cm = \(π\times(\frac{42}{2})^{2}\times21\)

= π(21)³ cm³ 

Since cylinders are filled by water completely, so volume of large cylinder = sum of these small cylinders 

∴ 2 πr³ = 2 × π(21)³ 

⇒ r = 21 cm 

∴ diameter of the cylindrical vessel = 42 cm