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.
Answers
Answer:
The rise in level of water in the vessel is 5.6 cm.
Step-by-step explanation:
Let 'h’ be the rise in level of water in the cylindrical vessel.
Given :
Diameter of the cylindrical vessel = 7 cm
Radius of the cylindrical vessel , R = 7/2 = 3.5 cm
Diameter of the spherical marble = 1.4 cm
Radius of the spherical marble , r = 1.4/2 = 0.7 cm
Volume of each marble = 4/ 3 × π r³
Volume of 150 marble = 150 × 4/ 3 × π (0.7)³ ………(1)
Volume of water displaced in the cylindrical vessel = πR²h = π(3.5)²× h ……….(2)
Since, volume of water displaced in the cylindrical vessel is equal to the volume of 150 spherical marbles
Volume of water displaced in the cylindrical vessel = Volume of 150 spherical marbles
π(3.5)²× h = 150 × 4/ 3 × π (0.7)³
(3.5)² × h = 150 × 4/ 3 × (0.7)³
h = [150 × 4 × (0.7)³] /[ (3.5)² × 3]
h = [150 × 4 × 0.7 × 0.7 × 0.7] /[ 3.5 × 3.5 × 3]
h = (50 × 4 × 0.7) / ( 5 × 5)
h = (200× 0.7)/ 25 = 8 × 0.7 = 5.6
h = 5.6 cm
Hence, the rise in level of water in the vessel is 5.6 cm.
HOPE THIS ANSWER WILL HELP YOU….
Here is your answer
Diameter of the spherical marble = 1.4 cm
Radius of the marble = 0.7 cm
Volume of each marble = 4 3 × π × r3 = 4 3 × 22 7 × (0.7)3 = 1.44
Volume of 150 marbles = 1.44 × 150 = 216 cu cm
Let the rise in level of water in the cylindrical vessel = 'h' cm
Diameter of the vessel = 7 cm
Radius of the vessel = 3.5 cm
Volume of the increased level of the water = π × r2 × h
= 22 7 × (3.5)2 × h
Volume of the increased level of the water = Volume of 150 marbles 22 7 × (3.5)2 × h = 216
⇒ h = 5.6 cm
Therefore, the rise in level of water in the vessel = 5.6 cm.
Hope its help you