Problem from RS Aggarwal book, problem number 30, page number 812, exercise 17B, chapter volume and surface area of solid.
Chapter Mensuration
Deepak BoraNewbie
Marbles of diameter 1.4 cm are dropped into a cylindrical beaker of diameter 7 cm, containing some water. Find the number of marbles that should be dropped into the beaker so that the water level rises by 5.6 cm.
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solution
given data,
Diameter of each marble = 1.4 cm
Radius of each marble = 0.7 cm
Volume of each marble = [4/3] πr³
= [4/3] π[0.7]³
The water rises as a cylindrical column.
Volume of cylindrical column filled with water = πr²h
= π 2² ×5. 6
Total number of marbles = Volume of cylindrical water column/Volume of marble
= [ π 2² ×5. 6] / [ [4/3] π[0.7]³ ]
= 150
∴ Total number of marbles are 150