Question

What is the maximum volume of a square pyramid that can fit inside a cube with a side length of 24 cm?

Answer 1

so, hmm notice the picture below

a cube is just a rectangular prism, with all equal sides, if one side is 24, all are 24

now, the base of the largest pyramid then, is just a 24x24, and the height, will also be 24

thus
`\bf \textit{volume of a pyramid}\\\\ V=\cfrac{1}{3}Bh\qquad \begin{cases} B=\textit{base area}\\ h=height\\ ----------\\ B=24\cdot 24\\ h=24 \end{cases}\implies V=\cfrac{1}{3}\cdot 24\cdot 24\cdot 24`