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