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

Answer:

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

Step-by-step 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

$\text{Volume of a Pyramid}=\dfrac{1}{3}*Base Area*Height$

$\text{Volume of One Pyramid}=\dfrac{1}{3}*h^2*Height$

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

Since Volume of the Cube = Volume of Six Square Pyramids

Then:

$2h^2*Height=h^3\\Height=\dfrac{h^3}{2h^2} \\ Height of each pyramid =\dfrac{1}{2}h \:Units$

Answer 2

Answer:

A= the Height is 1/2

Step-by-step explanation:

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