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

Explanation:

Given

the side length of the cube
`a=(1)/(4)\ inch`

The dimension of the box is
`1*3 (3)/(4)* 1 (1)/(2)=1*(15)/(4)*(3)/(2)\ inch^3`

the volume of each cube
`=a^3=((1)/(4))^3`

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

`\Rightarrow (1* (15)/(4)*(3)/(2))/((1)/(4)*(1)/(4)*(1)/(4))=360`

Therefore 360 cubes can be fit into the box