Q. 204.5( 2 Votes )

# A sphere of diame

Answer :

Given: Diameter of a sphere: 18cm ⇒ radius = = 9cm

Diameter of Cylindrical vessel: 36cm ⇒ radius = = 18cm

It is given that Sphere is dropped into the cylindrical vessel containing some water.

∴ Volume of sphere = Volume of water in Cylinder displaced (raised)

Let V_{1} be the volume of the Sphere

∴ V_{1} = × π × (r_{1})^{3}

V_{1} = × π × 9^{3}

Let V_{2} be the volume of the water displaced in the cylindrical vessel

∴ V_{2} = π × (r_{2})^{2} × h (here r_{2} is the radius of the Cylinder and h is the level of water raised in the vessel after dropping the sphere into the cylindrical vessel)

V_{2} = π × 18^{2} × h

Since V_{1}=V_{2}

× π × 9^{3} = π × 18^{2} × h

h = = = 3cm

∴ The water level rises by 3cm when the dropped sphere is completely submerged in the cylindrical vessel.

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