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

Ans:  Let’s draw a diagram to understand the question:

Given that the diameter of the marble = 1.4 cm = 14 mm

Therefore, the radius of the marble = 7 mm

Also, the diameter of the cylinder = 7 cm = 70 mm

Therefore, the radius of the cylinder = 35 mm

Step 1: Let’s start from volume of each marble.

We know that the volume of a sphere = r³

Hence, volume of each marble =

Hence, volume of 150 marbles =150

Next, let’s assume that after immersing 150 marbles, water level rises by h mm.

We know that the volume of the cylinder =

Hence, the volume of the water level risen in the cylinder =

Since the volume of 150 marbles = Volume of water level risen in the cylinder

h = 56 mm = 5.6 cm

Therefore, the rise of the water level is 5.6 cm.

(Note: We do not solve above complex calculation unnecessarily. It will consume time whereas most of the terms will be cancelled when we calculate height of water rise in cylinder)