Question

how many 1/4 inch cubes does it take to fill a box with width 1 inches, length 3 3/4 and height 1 1/2 inches?

Answer 1

Answer: 360

Step-by-step explanation:

Given

the side length of the cube $a=\frac{1}{4}\ inch$

The dimension of the box is $1\times3 \frac{3}{4}\times 1 \frac{1}{2}=1\times\frac{15}{4}\times\frac{3}{2}\ inch^3$

the volume of each cube $=a^3=(\frac{1}{4})^3$

No. of cubes that can be fit into the box $=\dfrac{\text{vol. of box}}{\text{vol. of each cube}}$

$\Rightarrow \dfrac{1\times \frac{15}{4}\times\frac{3}{2}}{\frac{1}{4}\times\frac{1}{4}\times\frac{1}{4}}=360$

Therefore 360 cubes can be fit into the box