Answer to Question #124932 in Geometry for Jonathan

Question

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

Answer 1

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

The square pyramid has the square base of area $S=a^2 = 9\,\mathrm{cm}^2$ and the height of $a$ . The volume of a pyramid is $V_p = \dfrac13\cdot S\cdot h = \dfrac13\cdot 9\,\mathrm{cm}^2\cdot 3\,\mathrm{cm} = 9\,\mathrm{cm}^3.$