Question

Find the maximum number of rectangular blocks measuring $3$ inches by $2$ inches by $1$ inch that a cube-shaped box whose interior measures $6$ inches on an edge can accomodate within it.

• A. $24$
• B. $28$
• C. $30$
• D. $36$

Answer 1

The correct option is D $36$

Number of blocks that can be accommodated $=\frac{\text{Volume of cube box}}{\text{Volume of one rectangular block}}$
Volume of a cube of edge a $=a^3$
Volume of a cuboid of length $\left(l\right)$, breadth $\left(b\right)$ and height $\left(h\right)=l\times b\times h$.
Hence, number of blocks that can be accommodated $=\frac{6\times 6\times 6}{3\times 2\times 1}=36$