Question

Six pyramids are shown inside of a cube. The height of the cube is h units. Six identical square pyramids can fill the same volume as a cube with the same base. If the height of the cube is h units, what is true about the height of each pyramid

Answer 1

The height of squared pyramid is $\frac{1}{3}h$ unit.

What is the volume of a cube?

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 $= (side)^3 \ unit^3$

Given the height of cube is $h$ unit.

Volume of cube is $h^3 \ unit^3$

Let the height of squared pyramid is $x$ unit

Volume of squared pyramid is $\frac{1}{3} h^{2} \times x \ unit^3$

According to the question, we have

Volume of cube = $6 \times$ volume of squared pyramid

$\Rightarrow h^3=6 \times \frac{1}{3}h^2 \times x\\\Rightarrow h^3=2 \ h^2 \times x\\\Rightarrow h=2x\\\Rightarrow x= \frac{1}{2}h$

Therefore, the height of squared pyramid is $\frac{1}{3}h$ unit.

To learn more about squared pyramid from the given link

brainly.com/question/27476449

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