Question

A cylinder shaped vessel of diameter 7cm is filled
with water 150 marbles of diameter 1.4cm is fully
immersed
in the water in
in the vessel find the
height of level of the water increased​

Answer 1

Given,

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

Answer:

Step-by-step explanation:

diameter of marble = 1.4 cm

radius of marble = 0.7 cm

number of marbles = 150

diameter of cylinder = 7cm

radius of cylinder = 3.5cm

Let the height of the water raised when 150 spheres are dropped in the vessel.

volume of 150 marbles = volume of water raised by height 'h' inside the vessel

150 * 4 / 3 * pie * 0.7 * 0.7 * 0.7 =pie * 3.5 * 3.5 *h [vol. of sphere = (4/3) pie r3 ; vol. of cylinder = pie r2 h]

50 * 4 * (0. 7)3 = (3.5)2 * h

200 * 0.343 = 12.25 * h

68.6 / 12.25 = h

5.6 = h

Height of water raised(h) = 5.6 cm