Question

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 ______.

Options

• \[\sqrt{\frac{a^{3}}{\pi r}}\]

• \[\frac{a}{\sqrt{\pi r}}\]

• \[\frac{a^{3}}{\pi r^{2}}\]

• \[\frac{\pi r^{2}}{a}\]

Answer 1

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 \[\underline{\boldsymbol{\frac{a^3}{\pi r^2}}}\].

Explanation:

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 = \[\frac{a^{3}}{\pi r^{2}}\]