Six square-based pyramids fit exactly onto the six faces of a cube with sides of 4 cm. lf the volume of the figure formed is 256 cu. cm, how do you find the height of each pyramid?

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Answer 1 · 2016-11-28T15:04:32

The height is #6cm#. See explanation.

If we denote:

#V_t# - total volume of the figure,

#V_c# - cube's volume

#V_p# - one pyramid's volume

The total volume can be calculated as:

#V_t=V_c+6*V_p#

#V_c=4^3=64#

#V_p=1/3*4^2*h=16/3h#

Knowing that the total volume is #256 cm^3# we can write:

#64+6*(16h)/3=256#

#64+32h=256#

If we divide both sides by #32# we get:

#2+h=8#

#h=6#

Answer: The heigt of the pyramid is #6cm#