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.

Question

Mathematics

Kobe Tran

18 January, 21:55

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.

+5

Answers (2)

Know the Answer?

Hezekiah Tapia · Answer 1

The answer is A. The height of each pyramid is 1/2h units.

Peyton Durham · Answer 2

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.