The volume of a cube is 512 cm3. Find its total surface area.

The volume of a cube is given by the formula:

\[
V = s^3
\]

where \( s \) is the side length of the cube. Given that the volume is \( 512 \, \text{cm}^3 \), we can find \( s \) by taking the cube root of the volume:

\[
s = \sqrt[3]{512} = 8 \, \text{cm}
\]

Now, to find the total surface area \( A \) of the cube, we use the formula:

\[
A = 6s^2
\]

Substituting \( s = 8 \, \text{cm} \):

\[
A = 6 \times (8)^2 = 6 \times 64 = 384 \, \text{cm}^2
\]

So, the total surface area of the cube is \( 384 \, \text{cm}^2 \).

Would you like further details on the steps or have any questions?

Here are 5 related questions to expand on this topic:
1. What is the length of the diagonal of a face of the cube?
2. How does the surface area change if the side length is doubled?
3. What is the volume of a cube with a surface area of 150 cm²?
4. If the volume of the cube is tripled, how does the side length change?
5. How do you find the surface area of a rectangular prism?

**Tip:** The surface area of a cube grows much faster than its volume as you increase the side length, since surface area depends on \( s^2 \) while volume depends on \( s^3 \).

The volume of a cube is 512 cm³. Find its total surface area.

Learn how to calculate the total surface area of a cube given its volume of 512 cm³. This detailed solution covers key geometry concepts, including volume and surface area, and uses the formulas V = s³ and A = 6s². Suitable for students in Grades 6-8.

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