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)