Mathematics
savahannag
15

The volume of a pyramid that fits exactly inside a cube is 49 cubic feet. What is the volume of the cube? 7 cubic feet 147 cubic feet 241 cubic feet 2401 cubic feet

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(1) Answers
ElizbethLiddle208

If the pyramid fits perfectly in a cube, this means that its base is a square and its height has the same value as the side of the square. Let x be the measure of the sides of the cube. The volume of the cube (Vc),                                     Vc = x³   ; 49 ft³ = x³    ; x = 49^(1/3) The volume of the pyramid is,                                 Vp = (1/3)(x²)(x) = (1/3)(x³) Substituting the known values,                                  Vp = (1/3)((49^(1/3))³ = 16 1/3 ft³ Thus, the volume of the pyramid is approximately 16.33 ft³.

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