The cube has the dimensions of:
[tex]1.26m \ by \ 1.26m \ by \ 1.26m[/tex]
Explanation:
A cube is a prism whose sides all have the same length. So the dimension of this cube will be given by one of its sides. For any object that is submerged in water, the volume of the displacement liquid equals the volume of the object.
[tex]For \ any \ cube \ the \ volume \ in \ terms \ of \ one \ side \ (s) \ is: \\ \\ V=s^3[/tex]
Suppose the volume of the tank when full is [tex]16m^3[/tex], so if it is 5/8 filled with water, then:
[tex]V_{5/8}=\frac{5}{8}(16) \\ \\ V_{5/8}=10m^3[/tex]
When the metal cube is placed in the tank, it is 3/4 full:
[tex]V_{3/4}=\frac{3}{4}(16) \\ \\ V_{3/4}=12m^3[/tex]
So the difference between these two volumes is the displacement volumen that equals the volume of the cube:
[tex]V=V_{3/4}-V_{5/8} \\ \\ V=12-10 \\ \\ V=2m^3[/tex]
So, the side of the cube is:
[tex]s=\sqrt[3]{2} \\ \\ \boxed{s\approx 1.26m}[/tex]
Learn more:
Volume of a sphere: https://brainly.com/question/12503759
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