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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? A. The height of each pyramid is h units.
B. The height of each pyramid is h units.
C. The height of each pyramid is h units.
D. The height of each pyramid is h units.

Respuesta :

W0lf93
To determine the height of each of the pyramid with respect to the height of the cube, we use the relationship between the volumes of the shapes. We do as follows:

Volume of the cube = h^3
Volume of all pyramid = 6 (h^2 (s/3)) where s is the height of a pyramid

Equating the two equations since they are equal,

h^3 = 6 (h^2 (s/3))

Simplifying,

h = 2s
s = h/2

Therefore, the height of each of the pyramid is equal to one-half units of the height of the cube.
akposevictor

The statement that is true about the height of the square pyramid is: height of each square pyramid is 1/2h units.

What is the Volume of a Square Pyramid?

  • Volume of Square Pyramid that has a side, a, and height, H, is given as: V = 1/3(a²)(H).

Volume of Cube

  • Where a is the length of each side of the cube, Volume of the cube is, V = a³, which is also V = h³.

Given that the height of the cube that has same base with the square pyramid is, h units.

Thus:

Volume of Cube = h³

Volume of square pyramid = 1/3(h²)(H)

If 6 of the volume equals a volume of the cube, therefore:

6(1/3)(h²)(H) = h³

  • Simplify and make H the subject of the formula

2(h²)(H) = h³

  • Divide both sides by 2h²:

H = h³/2h²

H = h/2

H = 1/2h

Therefore, the statement that is true about the height of the square pyramid is: height of each square pyramid is 1/2h units.

Learn more about square pyramid on:

https://brainly.com/question/25823102

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