Question

How many cubes with side lengths of 1/2 cm does it take to fill up the prism

Answer 1

24 cubes can filled up the prism

Solution:

The image of the question is attached below.

Given data:

Length of the prism = 2 cm

Breadth of the prism = 1 cm

Height of the prism = $\frac{3}{2}$ cm

Volume of the prism = length × breadth × height

                                   $=2\times 1\times \frac{3}{2}$

                                   $=3$ cubic cm

Volume of the prism = 3 cubic cm

Side length of the cube = $\frac{1}{2}$ cm

Volume of the cube = side × side × side

                                 $=\left(\frac{1}{2}\right)^{3}$

                                 $=\frac{1}{8}$ cubic cm

Volume of the cube =  $\frac{1}{8}$ cm

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

                          $=\frac{3}{\frac{1}{8} }$

                          $=3\times8$

                          $=24$

Number of cubes = 24

Hence 24 cubes can filled up the prism.