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To find the value of \( t \), we can use the formula for the volume of a cube, which is:

\[
V = t^3
\]

Given that the volume of the cube is 512 cubic centimeters, we can set up the equation:

\[
t^3 = 512
\]

Now, solve for \( t \) by taking the cube root of both sides:

\[
t = \sqrt[3]{512}
\]

Since \( 512 = 8^3 \), we have:

\[
t = 8 \text{ centimeters}
\]

Therefore, the value of \( t \) is \( 8 \) centimeters.

Would you like further details or have any questions?

Here are 5 related questions to consider:
1. What is the formula for the surface area of a cube with side length \( t \)?
2. If the side length \( t \) was doubled, what would the new volume be?
3. How would the volume change if \( t \) was halved?
4. What is the cube root of 729? How does it relate to finding the side length of a cube with volume 729?
5. Can you express the volume formula for a rectangular prism instead of a cube?

**Tip:** To solve cube volume problems, always remember to take the cube root to find the side length.

The volume of this cube is 512 cubic centimeters. What is the value of t?

Learn how to find the side length of a cube with a volume of 512 cubic centimeters. This problem covers key geometric concepts, including the volume formula for a cube and the cube root theorem. Suitable for students in Grades 6-8.

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