Question

a rectangular vessel 33 cm into 18 cm into 12 cm is full of water if the water is poured into an empty cylindrical vessel of radius 9 cm find the height of water in the cylindrical vessel



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Answer 1

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 the cylindrical vessel is 42 cm

Answer 2

r3=(21)3

r=21

so d= 42.