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A cylindrical container has sufficient water to submerge a solid cubical object of its each edge a cm. If the radius of the container is r cm, the rise in level (h cm) of water in the container is :

  1. a3πr\sqrt{\dfrac{a^3}{πr}}

  2. aπr\dfrac{a}{\sqrt{πr}}

  3. a3πr2\dfrac{a^3}{πr^2}

  4. πr2a\dfrac{πr^2}{a}

A cylindrical container has sufficient water to submerge a solid cubical object of its each edge a cm. If the radius of the container is r cm, the rise in level (h cm) of water in the container is : Cylinder, Cone, Sphere, Concise Mathematics Solutions ICSE Class 10.

Mensuration

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Answer

Suppose rise in level of water be h cm.

Increase in volume of cylinder = πr2h.

Given,

Edge of cubical solid submerged = a cm.

Volume of cubical solid submerged = a3

We know that,

Volume of cubical solid submerged = Increase in volume of cylinder

⇒ a3 = πr2h

⇒ h = a3πr2\dfrac{a^3}{πr^2}.

Hence, Option 3 is the correct option.

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