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7. Relate the volume of the cube to the length

of each edge.
V = 8 cm³
Edge length Edge length Edge length
cm X
cm X
√8 = 2
cm

1 Answer

3 votes
It seems like you're working with a cube and its volume. Here's how the volume of the cube is related to the length of each edge:

The volume \(V\) of a cube is given by the formula:
\[ V = \text{edge length} \times \text{edge length} \times \text{edge length} \]

In your case, you've mentioned that the volume \(V\) is 8 cm³, and you want to find the length of each edge (\(X\) cm).

So, we have:
\[ V = X \times X \times X = X^3 \]

Given that \(V = 8 \, \text{cm}³\), you can solve for \(X\) using the equation:
\[ X^3 = 8 \]

Taking the cube root of both sides:
\[ X = \sqrt[3]{8} \]

Since \(8 = 2^3\), you can simplify further:
\[ X = \sqrt[3]{2^3} = 2 \]

Therefore, the length of each edge of the cube is 2 cm.

In summary, the volume of a cube is related to the length of each edge by the formula \(V = \text{edge length}^3\), and in your case, with a volume of 8 cm³, the length of each edge is 2 cm.
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