Answer :
Certainly! Let's solve this step-by-step:
1. Determine the dimensions of the original chocolate bar:
- Length = 16 cm
- Width = 8 cm
- Height = 4 cm
2. Calculate the volume of the original chocolate bar:
The volume [tex]\( V \)[/tex] of a rectangular prism (or bar) can be calculated using the formula:
[tex]\[ V = \text{Length} \times \text{Width} \times \text{Height} \][/tex]
Plugging in the dimensions:
[tex]\[ V = 16 \, \text{cm} \times 8 \, \text{cm} \times 4 \, \text{cm} = 512 \, \text{cubic centimeters (cm}^3\text{)} \][/tex]
3. Determine the volume of each chocolate cube:
Given that the total volume of the chocolate bar is divided into 8 cubes:
[tex]\[ \text{Volume of each cube} = \frac{\text{Total Volume of the bar}}{\text{Number of cubes}} = \frac{512 \, \text{cm}^3}{8} = 64 \, \text{cm}^3 \][/tex]
4. Determine the length of each side of a cube:
Since each cube is a perfect cube, the volume of a cube is given by:
[tex]\[ \text{Volume} = \text{side length}^3 \][/tex]
Let the side length of each cube be [tex]\( s \)[/tex]. Then:
[tex]\[ s^3 = 64 \, \text{cm}^3 \][/tex]
5. Solve for the side length [tex]\( s \)[/tex]:
To find [tex]\( s \)[/tex], we take the cube root of 64:
[tex]\[ s = \sqrt[3]{64} = 4 \, \text{cm} \][/tex]
Thus, the length of each side of the cube is approximately [tex]\( 4 \)[/tex] cm.
1. Determine the dimensions of the original chocolate bar:
- Length = 16 cm
- Width = 8 cm
- Height = 4 cm
2. Calculate the volume of the original chocolate bar:
The volume [tex]\( V \)[/tex] of a rectangular prism (or bar) can be calculated using the formula:
[tex]\[ V = \text{Length} \times \text{Width} \times \text{Height} \][/tex]
Plugging in the dimensions:
[tex]\[ V = 16 \, \text{cm} \times 8 \, \text{cm} \times 4 \, \text{cm} = 512 \, \text{cubic centimeters (cm}^3\text{)} \][/tex]
3. Determine the volume of each chocolate cube:
Given that the total volume of the chocolate bar is divided into 8 cubes:
[tex]\[ \text{Volume of each cube} = \frac{\text{Total Volume of the bar}}{\text{Number of cubes}} = \frac{512 \, \text{cm}^3}{8} = 64 \, \text{cm}^3 \][/tex]
4. Determine the length of each side of a cube:
Since each cube is a perfect cube, the volume of a cube is given by:
[tex]\[ \text{Volume} = \text{side length}^3 \][/tex]
Let the side length of each cube be [tex]\( s \)[/tex]. Then:
[tex]\[ s^3 = 64 \, \text{cm}^3 \][/tex]
5. Solve for the side length [tex]\( s \)[/tex]:
To find [tex]\( s \)[/tex], we take the cube root of 64:
[tex]\[ s = \sqrt[3]{64} = 4 \, \text{cm} \][/tex]
Thus, the length of each side of the cube is approximately [tex]\( 4 \)[/tex] cm.
