Question

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

• A. 102 cubes
• B. 104 cubes
• C. 100 cubes
• D. 108 cubes

Answer 1

The correct option is D 108 cubes

The given box is


Length of the box(L) = 4 in

Height of the box(H) = 3 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 =
$(\frac{2}{3}{)}^3$

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