Pyramid in cube

In a cube with an edge 12 dm long, we have an inscribed pyramid with the apex at the center of the cube's upper wall. Calculate the volume and surface area of the pyramid.

Correct result:

V =  576 dm3
S =  465.9938 dm2

Solution:

a=12 h=12 V=a2 h/3=122 12/3=576 dm3
h2=h2+(a/2)2=122+(12/2)2=6 513.4164 S2=a h2/2=12 13.4164/2=36 580.4984 S=a2+4 S2=122+4 80.4984=465.9938 dm2



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