Question

A cube of side 6cm is immersed completely in a cylindrical jar such that water does not overflow. If the area of base of the jar is 120 cm2, find the rise in the water level in the jar.

Answer 1

$\huge\mathfrak\blue{Answer:}$

Given:

• We have been a cube of side 6 cm
• It is completely immersed in a cylindrical jar having base area 120 cm²

To Find:

• We have to find the rise in water level when cube in completely immersed

Solution:

We have been given that for a cube

Side of cube = 6 cm

Area of base of cylinder = 120 cm²

Volume of Cube can be calculated as

$\large\boxed{\sf{\green{Volume \: of \: Cube = (Side)^3}}}$

$\implies \sf{Volume \: of \: Cube \: (V) = (6)^3}$

$\implies \sf{V = 216 \: cm^3}$

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$\underline{\large\mathfrak\orange{According \: to \: the \: Question:}}$

When cube is completely immersed in the cylindrical jar level of water is raised

The rise in level of water Will be due to the volume of immersed cube as:

$\implies \boxed{\sf{\pink{Volume \: of \: water \: raised = Volume \: of \: Cube }}}$

$\implies \sf{Volume = 216 cm^3}$

$\implies \sf{Area \: of \: Base\times Height = 216 cm^3}$

$\implies \sf{120 \times Height = 216 cm^3}$

$\implies \sf{Height = \dfrac{216}{120}}$

$\implies \sf{Height = 1.8 \: cm}$

Rise in level of water when cube is completely immersed in cylindrical jar is 1.8 cm

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$\huge\underline{\sf{\red{A}\orange{n}\green{s}\pink{w}\blue{e}\purple{r}}}$

$\large\boxed{\sf{\red{Rise \: in \: water \: level = 1.8 cm}}}$

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