Question

Stephanie puts 30 cubes in a box. The cubes are inch on each side. The box holds 2 layers

with 15 cubes in each layer. What is the volume of the box?

Answer 1

The volume of the box is
`\( 3(3)/(4) \)` cubic inches.

The problem is asking for the volume of a box that Stephanie is using to store cubes. Each cube has a side length of
`\( (1)/(2) \)` inch. There are two layers of cubes in the box, with 15 cubes in each layer, making a total of 30 cubes.

To find the volume of the box, we can follow these steps:

1. Calculate the volume of one cube.

2. Calculate the volume of all the cubes.

3. Since the cubes perfectly fit in the box, the volume of all the cubes will be equal to the volume of the box.

Step 1: Volume of one cube

The volume V of a cube can be found using the formula
`\( V = a^3 \),`where a is the length of each side of the cube.

For one cube with side length
`\( (1)/(2) \)` inch:

`\[ V = \left((1)/(2)\right)^3 \]`

`\[ V = (1)/(2) * (1)/(2) * (1)/(2) \]`

`\[ V = (1)/(8) \text{ cubic inches} \]`

Step 2: Volume of all cubes

Since there are 30 cubes, we multiply the volume of one cube by 30:

`\[ V_(total) = 30 * (1)/(8) \text{ cubic inches} \]`

`\[ V_(total) = (30)/(8) \text{ cubic inches} \]`

`\[ V_(total) = (15)/(4) \text{ cubic inches} \]`

`\[ V_(total) = 3(3)/(4) \text{ cubic inches} \]`

Answer 2

`11.25\: {in}^(3)`

Explanation:

Since, box contains two layers of cubes and each layer has 15 cubes.

So, length = 15*1/2 in = 7.5 in,

width = 3*1/2 in = 1.5 in

height = (1/2 + 1/2) = 1 inch

Volume of box = lbh

= 7.5* 1.5 *1

= 11.25 cubic inches