Question
How many blocks are along the edges of a Rubik's cube that consists of 125 blocks?
Answers
Answered by
GPT-4o mini
To solve the problem, we first need to determine the dimensions of a Rubik's cube that consists of 125 blocks (also referred to as smaller cubes). A Rubik's cube can be represented as a cube made up of smaller cubes arranged in a larger cube structure.
The total number of smaller cubes in a Rubik's cube can be expressed as \( n^3 \), where \( n \) is the number of smaller cubes along each edge of the Rubik's cube. In this case, we have:
\[
n^3 = 125
\]
To find \( n \), we take the cube root of 125:
\[
n = \sqrt[3]{125} = 5
\]
This means that the Rubik's cube is composed of 5 smaller cubes along each edge.
Next, we need to determine how many cubes are located along the edges of the Rubik's cube. A cube has 12 edges and each edge contains \( n \) smaller cubes. Therefore, the total number of smaller cubes along all the edges is calculated as follows:
\[
\text{Total cubes along the edges} = \text{Number of edges} \times n = 12 \times 5 = 60
\]
Thus, the answer to the question is:
\[
\boxed{60}
\]
The total number of smaller cubes in a Rubik's cube can be expressed as \( n^3 \), where \( n \) is the number of smaller cubes along each edge of the Rubik's cube. In this case, we have:
\[
n^3 = 125
\]
To find \( n \), we take the cube root of 125:
\[
n = \sqrt[3]{125} = 5
\]
This means that the Rubik's cube is composed of 5 smaller cubes along each edge.
Next, we need to determine how many cubes are located along the edges of the Rubik's cube. A cube has 12 edges and each edge contains \( n \) smaller cubes. Therefore, the total number of smaller cubes along all the edges is calculated as follows:
\[
\text{Total cubes along the edges} = \text{Number of edges} \times n = 12 \times 5 = 60
\]
Thus, the answer to the question is:
\[
\boxed{60}
\]
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