Question

A cube has a side length of 1/3 inch .. how many blocks with a side length of 1/6 inch would it take

to fill the cube

Answer 1

let's bear in mind that a rectangular prims, namely a box, has a volume of length*width*height.

a cube is a rectangular prism with all sides equal, so if one sides is 1/3, all sides are 1/3, that means

`\bf \stackrel{\textit{volume of large cube}}{\cfrac{1}{3}\cdot \cfrac{1}{3}\cdot \cfrac{1}{3}\implies \cfrac{1}{27}}~\hspace{10em} \stackrel{\textit{volume of small cube}}{\cfrac{1}{6}\cdot \cfrac{1}{6}\cdot \cfrac{1}{6}\implies \cfrac{1}{216}} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \stackrel{\textit{how many times does }(1)/(216)\textit{ go into }(1)/(27)?}{\cfrac{1}{27}/ \cfrac{1}{216}\implies \cfrac{1}{27}\cdot \cfrac{216}{1}}\implies \cfrac{216}{27}\implies 8`