Question

a rectangular vessel 22 cm into 16 cm into 14 cm is full of water. if the total water is poured into an Empty cylindrical vessel of radius 8 cm, find the height of water in the cylindrical vessel

Answer 1

First,

a rectangular (cuboidal) vessel is full of water.

Volume of cuboid = L × B × H

=> Volume of cuboid = 22 × 16 × 14

=> Volume of cuboid = 4928 cm³

Now since it's full of water,

=> Volume of water = 4928 cm³

Again, given that the water is poured in a cylindrical vessel.

The volume will remain the same as the water is completely poured.

We know that, volume of cylinder = πr²h

But here it asks for height of Water

=> volume of water = πr²h

But volume of water = 4928
and radius = 8

Taking π as 22/7 we get,

$4928 = \frac{22}{7} \times {8}^{2} \times h \\ \\ = > 4928 = \frac{22}{7} \times 64 \times h \\ \\ = > h = \frac{4928}{64} \times \frac{7}{22} \\ \\ = > h = \frac{4928 \times 7}{1408} \\ = > h = 3.5 \times 7 \\ \\ = > h = 24.5$
Hence, the height of water is 24.5 cm


Hope it helps dear friend

Answer 2

volume of the rect. vessel = lbh = 22 x 16 x 14 = 4928 cm³

volume of cylinder =  \pi r²h

according to the ques.

4928 = 22/7 x 8² x h

h = 4928 x 7/22 x 1/64 = 24.5 cm