Question

Answer is 5cm

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Answer 1

The height of the empty space in the rectangular container is 3 cm.

Let's find the empty space.

$\bold{\implies 6\times 6\times 3=108}$ cm³

The water rises to the top, so the empty space is completely filled. 17 cm³ overflows from the container.

Let's find the volume taken by the cube.

$\bold{\implies 108+17=125}$ cm³

Now the edge will be the cube root of the volume.

$\bold{\implies \sqrt[3]{125} =5}$ cm

Extra question.

Q. Can 17 cm³ overflow even if the cube cannot get submerged? Even if the height of the cube is small even if the cube isn't submerged, there will be an overflow.

A. Not possible.

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Let the height of the rectangular container be x.

Let's find the volume of the space.

$\bold{\implies 6\times6\times3}$

$\bold{\implies 108}$ cm³

Let's find how much the solid cube takes.

$\bold{\implies 5\times5\times x}$

$\bold{\implies 25x}$ cm³

The solid cube will fill the empty space and make the water overflow. Now, the volume of it should equal the volume it fills and the water overflows.

$\bold{\implies 25x=108+17}$

$\bold{\implies 25x=125}$

$\bold{\therefore x=5}$

This is the exact height of the cube.

We assumed that the cube isn't submerged, so this is not a solution.

It is not possible.

Answer 2

Step-by-step explanation:

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