Question

Ix 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.

Answer 1

height of each pyramid must be 3h units

Step-by-step explanation:

As we know that the volume of the cube is same as that of volume of square pyramid

so we have volume of the cube is given as

`V = h^3`

now if the base area of pyramid and the cube is same

so we will have

`V_(pyramid) = (1)/(3) Base\: Area * height`

`V_(pyramid) = (1)/(3) h^2 * y`

now since both have same volume

`(1)/(3)h^2 y = h^3`

`y = 3h`

height of each pyramid must be 3h units