Question

The number of cubes having side length $0.5$ units that can occupy the prism, as shown above, is .

• A. $432$
• B. $400$
• C. $512$

Answer 1

The correct option is A $432$

Given the prism with the dimensions as shown:

Here, we want to stack cubes of side length $0.5$ units.
$\therefore$ Let's calculate the number of cubes each side can accommodate.
For the side length as $4.5$ units.
Number of cubes that can be stacked on it $=\frac{4.5}{0.5}=9$
Number of cubes that can be stacked on the side having length $2$ units $=\frac{2}{0.5}=4$
And similarly, the number of cubes that can be stacked for the length $6$ units $=\frac{6}{0.5}$
$=12$
$\therefore$ Total number of cubes $=9\times 4\times 12$
$=432$ cubes.