Question #124932

Given a cube with a volume of 27 cm3, what is the volume of a square pyramid that can fit perfectly inside the cube?


3cm3

6cm3

9cm3

12cm3


1
Expert's answer
2020-07-02T19:02:47-0400

Let us determine the edge aa of the cube. The volume is V=a3=27,V=a^3=27, therefore a=273=3cm.a = \sqrt[3]{27} = 3\,\mathrm{cm}.

The square pyramid has the square base of area S=a2=9cm2S=a^2 = 9\,\mathrm{cm}^2 and the height of aa . The volume of a pyramid is Vp=13Sh=139cm23cm=9cm3.V_p = \dfrac13\cdot S\cdot h = \dfrac13\cdot 9\,\mathrm{cm}^2\cdot 3\,\mathrm{cm} = 9\,\mathrm{cm}^3.


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