Question

59. A cylindrical tank of base radius 21cm contains water. In that water, a metal block
of length 22cm, breadth 18 cm, height 7cm is dropped then what is increase in the
level of water in tank?​

Answer 1

Answer:

The level increase in water inside tank is 2 cm  .

Step-by-step explanation:

Given as :

The radius of cylindrical tank = r = 21 cm

Let The height of tank = h cm

So, The volume of cylindrical tank = V = π × radius² × height

i.e V = π × r² × h

Or, V = π × 21² × h            ........1

Again

A metal block is dropped inside tank

The length of metal box = l = 22 cm

The width of metal box = b = 18 cm

The height of metal box = h' = 7 cm

So, The volume of metal box = v = l × b × h'

i.e v =  22 cm × 18 cm × 7 cm

Or, v = 2770 cm²          ......2

Since the metal box is dropped in tank . so the level increase in water = the height of cylinder

i.e The volume of tank = volume of box

Or, from eq 1 and eq 2

π × 21² × h = 2770 cm²

or, 3.14 × 441 × h = 2770

Or, 1384.74 × h = 2770

i.e h = $\dfrac{2770}{1384.74}$

∴ h = 2.0003 ≈ 2 cm

So, The level increase in water inside tank = h = 2 cm

Hence, The level increase in water inside tank is 2 cm  . Answer