Question

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

Answer 1

as you know, a cube has all equal dimensions, thus length=width=height = x, check the picture below.

that means the square pyramid has a base of a 3x3 square, and its height is also 3, thus


`\bf \textit{volume of a pyramid}\\\\ V=\cfrac{1}{3}Bh~~ \begin{cases} B=area~of\\ \qquad its~base\\ h=height\\ ------\\ B=\stackrel{3* 3}{9}\\ h=3 \end{cases}\implies V=\cfrac{1}{3}(9)(3)`