A sphere of diameter 18cm is dropped into a cylindrical vessel of diameter 36 cm partly filled with water . if sphere is completely submerged , then how much does the water level rise ?
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Verified answer
Answer:
Thus, the rise in water level in the cylindrical vessel is 3cm.
solution →
Let r & R be the radius of the sphere and cylindrical vessel respectively.
Now, 2r=18cm⇒r=9cm
2R=36cm⇒R=18cm
Let the rise in water level in the cylindrical vessel be
′
h
′
cm.
Volume of sphere =
3
4
πr
3
Volume of liquid displaced in the cylindrical vessel =πR
2
h
If the sphere is completely submerged in the vessel, then volume of liquid displace in the cylindrical vessel = Volume of the sphere
∴πR
2
h=
3
4
πr
3
⇒(18)
2
×h=
3
4
×(9)
3
⇒h=
3×(18)
2
4×(9)
3
=3cm
Thus, the rise in water level in the cylindrical vessel is 3cm.
Answer:
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