Question

How many cubes are needed to fill in the rectangular prism?

Answer 1

8320 cubes can fit into the prism.

Solution:

Convert mixed fraction into improper fraction.

Length of the prism = 20 in

Width of the prism = 2 in

Height of the prism = $3\frac{1}{4}=\frac{13}{4}$ in

Volume of the prism = length × width × height

                                 $=20\times2\times\frac{13}{4}$

                                 = 130 in³

Volume of the prism = 130 in³

Length of the cube = $\frac{1}{4}$ in

Volume of the cube = length × length × length

                                 $=\frac{1}{4} \times\frac{1}{4} \times\frac{1}{4}$

                                 $=\frac{1}{64} \ \text{in}^3$

Volume of the cube = 0.015625 in³

$\text{Number of cubes}=\frac{\text{Volume of the prism}}{\text{Volume of cube}}$      

                            $=\frac{130}{0.015625}$

                            = 8320

Number of cubes = 8320

Hence 8320 cubes can fit into the prism.