The diameter of the cylinder = the height of the cylinder

 

⇒ h = 2r, where h – height of the cylinder and r – radius of the cylinder

 

We know that,

 

Volume of a cylinder = πr2h

 

So, volume of the cylindrical vessel = πr22r = 2πr3 (as h = 2r)….. (i)

 

Now,

 

Volume of each identical vessel = πr2h

 

Diameter = 42 cm, so the radius = 21 cm

 

Height = 21 cm

 

So, the volume of two identical vessels = 2 x π 212 × 21 ….. (ii)

 

Since the volumes on equation (i) and (ii) are equal

 

On equating both the equations, we have

 

2πr3= 2 x π 212 × 21

 

r3 = (21)3

 

r = 21 cm

 

So, d = 42 cm

 

Therefore, the diameter of t he cylindrical vessel is 42 cm