Question

A rectangular box has length 10 cm, width 8 cm and depth 3 cm. Find the size of the
biggest cube can be placed inside the box. Also calculate the number of such cubes that
can be placed inside the box. Hence, calculate the volume of the box that is unutilized.​

Answer 1

the volume of the rectangular box is

(10×8×3)cm³

= 240cm³

if we consider the size of a single side of a cube is

x

then its volume will be x³

so if we consider the value of x is- 6.2[we won't be able to make cube which has the side of more than that because the volume of that cube wouldn't fit in that rectangular box]

then its voulme will be 6.2³= 238.328cm³

then the unutilized space will be- (240-238.328)cm³

=1.672cm³ or 16.72mm³

we can say int he leftover place barely 17 cubes of with volume of 1mm³ can be fitted.