The box shown is used to ship miniature dice with side lengths of

1/2

in. ×

1/2

in. ×

1/2

in. how many dice cubes can fit in the box?

a) 480 dice

b) 1920 dice

c) 3840 dice

eliminate

d) 7680 dice

Using the volume of a rectangular prism, it is found that the number of cubes that can fit in a box is:

The volume of a rectangular prism of length l, width w and height h is given by:

For the dice, all dimensions are of , hence:

For the box, the dimensions are and , hence:

Applying the division of the volumes, we find how many dice can be put in the box:

Hence option C is correct.

To learn more about the volume of a rectangular prism, you can take a look at  link

Step-by-step explanation:

Let

x ----> the length of the third side of triangle in Lauren's sculpture

we know that

The Triangle Inequality Theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side

Applying the Triangle inequality Theorem

1)

Rewrite

2)

therefore

The possible values of x are