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?

Question

8459 views around the world

You can reuse this answer
Creative Commons License

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#