Question

How many sugar cubes with side length 2/3 in. can be filled in the below box in the form of a cuboid?

• A. 108 cubes
• B. 24 cubes
• C. 102 cubes
• D. 106 cubes

Answer 1

The correct option is A 108 cubes

The given box is

Height of the box (H) =3 in

Length of the box(L) = 4 in

Width of the box (W) = $\frac{8}{3}$ in

Volume of the box = L $\times$ W$\times$H

= 4 $\times$ $\frac{8}{3}$ $\times$ 3

= 32 cubic inches

Volume of 1 sugar cube =
$(\frac{2}{3}{)}^3$ cu in

= $\frac{2}{3}$ $\times$ $\frac{2}{3}$ $\times$$\frac{2}{3}$

= $\frac{8}{27}$

Number of cubes that can be filled = Volume of the box $÷$ volume of 1 sugar cube

= 32 $÷$ $\frac{8}{27}$ = 32 $\times$ $\frac{27}{8}$

= 108

Hence, 108 sugar cubes can be filled in the given box.