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Heidi is making a tower using sugar cubes. Each sugar cube has a side length of 1 cm. Each layer has 4 sugar cubes, arranged in a 2 by 2 pattern. The completed tower has a volume of 24 cm3. How many layers of sugar cubes are in the tower?

Respuesta :

MrRoyal

Answer:

3 layers

Step-by-step explanation:

Given

[tex]L = 1cm[/tex] --- side length of the cube

Each layer = 2 * 2 cube

[tex]Volume = 24cm^3[/tex]

Required

Determine the number of layers

First, we calculate the volume of each layer:

The length of the layer is:

[tex]Length = 2 * L[/tex]

[tex]Length = 2 * 1cm[/tex]

[tex]Length = 2cm[/tex]

Next, we calculate the volume of each layer:

[tex]Volume = Length^3[/tex]

[tex]Volume = (2cm)^3[/tex]

[tex]Volume = 8cm^3[/tex]

The number of layer is calculated by dividing the volume of the tower by the volume of each layer

[tex]Layers = \frac{24cm^3}{8cm^3}[/tex]

[tex]Layers = 3[/tex]

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