Question

150 spherical marbles,each of diameter 1.4cm, are dropped in a cylindrical vessel of diameter 7cm containing some water and are completely immersed in water. Find the
rise in the level of water in the vessel.

Hi dosto ✌✌

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Answer 1

ANSWER:-

Given:

150 spherical marbles, each of diameter 1.4cm, are dropped in a cylindrical vessel of diameter 7cm containing some water and are completely immersed in water.

To find:

Find the rise in the level of water in the vessel.

Solution:

⚫Diameter of spherical marbles= 1.4cm.

So, radius is 1.4/2

=) 0.7cm

⚫Diameter of cylindrical vessel= 7cm

So, radius= 7/2

=) 3.5cm

Therefore,

Volume of 150 spherical balls;

$= > 150 \times \frac{4}{3} \pi {r}^{3} \\ \\ = > \frac{150 \times 4 \times 22 \times 0.7 \times 0.7 \times 0.7}{3 \times 7} {cm}^{3} \\ \\ = > \frac{4527.6}{21} { cm}^{3} \\ \\ = > 215.6 {cm}^{3}$

Now,

Let the rise in level of water be h m

We know that, volume of cylinder;

=) πr²h

So,

Volume of rise in level of water;

$= > \frac{22}{7} \times 3.5 \times 3.5 \times h$

Volume of rise in level of water in the vessel = volume of 150 spherical balls;

$= > \frac{22}{7} \times 3.5 \times 3.5 \times h = 215.6 \\ \\ = > h = \frac{215.6 \times 7}{22 \times 3.5 \times 3.5} \\ \\ = > h = \frac{1509.2 \times 10}{269.5 \times 10 } \\ \\ = > h = \frac{15092}{2695} \\ \\ = > h = 5.6cm$

Thus,

The rise in the level of water in the vessel is 5.6cm.

Hope it helps ☺️