Question

150spherical marbles, each of diameter 1.4cm,are dropped in a cylinder vessel of diameter7cm containing some water, which are completely immersed in water. find the rise in the level of water in the vessel.

Answer 1

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Answer 2

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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