Question

A metal spherical ball of radius R units is submerged into a cuboidal water tank .The length of the base of the tank is 3R units and its breadth is 2R Units .What will be the rise in the level of water in the tank
A.πR/9 UNITS
B.πR/3 UNITS
C.2πR/9 UNITS
D.2πR/3 UNITS

Answer 1

Given :  A metal spherical ball of radius R units is submerged into a cuboidal water tank .The length of the base of the tank is 3R units and its breadth is 2R Units .What will be the rise in the level of water in the tank

To find : What will be the rise in the level of water in the tank

Solution:

Volume of metal spherical ball of radius R units = (4/3) πR³  cubic units

Volume of water Raised = (4/3) πR³    cubic units

Volume of water raised =  Length *  width * rise in the level of water in the tank

rise in the level of water in the tank = h

=> Volume of water raised =  3R * 2R  * h

Equating both

=> 3R * 2R  * h =  (4/3) πR³  

=> h  = (4/18) πR  

=> h  = (2/9) πR  

=> h  = 2πR/9  units

option C is correct

rise in the level of water in the tank  = 2πR/9  units

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