1. Marbles of diameter 1.4 cm are dropped into a
beaker containing some water and are fully
submerged. The diameter of the beaker is 7 cm.
Find how many marbles have been dropped in it
if the water rises by 5.6 cm.
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Answer:
Diameter of marble = 1.4 cm
Diameter of cylindrical beaker = 7 cm
Height of water level = 5.6 cm
Formula used:
The volume of sphere =
Volume of cylinder = πr2h
Explanation:
diameter of a marbles = 1.4 cm
∴ Radius of marble =
= 0.7 cm
So, volume of one marble =
Also, given diameter of beaker = 7 cm
∴ Radius of beaker =
= 3.5 cm
Height of water level raised = 5.6 cm
∴ Volume of the raised water in beaker = π r2 h
= π (3.5)2 × 5.6
= 68.6 π
Let n marbles be dropped into the beaker,
Hence n × volume of marble = volume of water raised
⇒
⇒
⇒ n = 150
Hence the number of marbles required are 150.
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