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 $6cm$