The height of squared pyramid is
unit.
<h3>What is the volume of a cube?</h3>
A cube is a solid three-dimensional object with six square faces or sides, three of which meet at each vertex. One of the five Platonic solids, the cube is the only regular hexahedron. It contains 8 vertices, 6 faces, and 12 edges.
Volume of cube ![= (side)^3 \ unit^3](https://tex.z-dn.net/?f=%3D%20%28side%29%5E3%20%5C%20unit%5E3)
Given the height of cube is
unit.
Volume of cube is ![h^3 \ unit^3](https://tex.z-dn.net/?f=h%5E3%20%5C%20unit%5E3)
Let the height of squared pyramid is
unit
Volume of squared pyramid is ![\frac{1}{3} h^{2} \times x \ unit^3](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B3%7D%20h%5E%7B2%7D%20%5Ctimes%20x%20%5C%20unit%5E3)
According to the question, we have
Volume of cube =
volume of squared pyramid
![\Rightarrow h^3=6 \times \frac{1}{3}h^2 \times x\\\Rightarrow h^3=2 \ h^2 \times x\\\Rightarrow h=2x\\\Rightarrow x= \frac{1}{2}h](https://tex.z-dn.net/?f=%5CRightarrow%20h%5E3%3D6%20%5Ctimes%20%5Cfrac%7B1%7D%7B3%7Dh%5E2%20%5Ctimes%20x%5C%5C%5CRightarrow%20h%5E3%3D2%20%5C%20h%5E2%20%5Ctimes%20x%5C%5C%5CRightarrow%20h%3D2x%5C%5C%5CRightarrow%20x%3D%20%5Cfrac%7B1%7D%7B2%7Dh)
Therefore, the height of squared pyramid is
unit.
To learn more about squared pyramid from the given link
brainly.com/question/27476449
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