The volume of a cube is 54 cubic feet. What is the volume of a pyramid that fits exactly inside the cube? Provide an explanation and proof for your answer to receive full credit.
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OpenStudy (anonymous):
@AliceAlexis
OpenStudy (anonymous):
@xostarbucks
OpenStudy (anonymous):
@triciaal
OpenStudy (triciaal):
a cube has all 3 dimensions equal
what is the formula for the volume of the pyramid?
OpenStudy (anonymous):
V = 1 over 3(B)(h)
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OpenStudy (triciaal):
V = 1/3*Bh where B is the base area
OpenStudy (anonymous):
im not sure
OpenStudy (triciaal):
volume of pyramid is 1/3 the volume of the cube
because wow i can explain this one
B = length * width and because the cube fits then the length and the width are equal
the height is also the same as the cube since the cube fits
the volume of pyramid is 1/3 *(l^2)*l = 1/3*l^3
volume of the cube is l^3 for a cube all the sides are equal
l = length
OpenStudy (triciaal):
correction the pyramid fits inside the cube
OpenStudy (triciaal):
volume of pyramid = 1/3 volume of cube = 1/3*54 = 18
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