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? The height of each pyramid is One-halfh units. The height of each pyramid is One-thirdh units. The height of each pyramid is One-sixthh units. The height of each pyramid is h units.

Answer 1

A= the Height is 1/2

Explanation:

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Answer 2

(A)The height of each pyramid is One-half h units.

Explanation:

Height of the Cube = h units

Volume of the Cube
`=h^3 $ cubic units`

If Base of the cube =Base of the square pyramid

Base of the square pyramid = h units

`\text{Volume of a Pyramid}=(1)/(3)*Base Area*Height`

`\text{Volume of One Pyramid}=(1)/(3)*h^2*Height`

`\text{Volume of Six Pyramids}=6*(1)/(3)*h^2*Height\\=(2h^2*Height)\:cubic\:units`

Since Volume of the Cube = Volume of Six Square Pyramids

Then:

`2h^2*Height=h^3\\Height=(h^3)/(2h^2) \\$Height of each pyramid =(1)/(2)h \:Units`