https://file.aiquickdraw.com/mathbot/file/1726890961909r31lo218.jpg

The question asks for the surface area of a cube that has a volume of 512 cm³. Here's how we can solve this:

### Step-by-Step Solution:
1. **Formula for the Volume of a Cube:**
   The volume \( V \) of a cube is given by:
   \[
   V = s^3
   \]
   where \( s \) is the length of one side of the cube.

2. **Find the Side Length \( s \):**
   We are given that the volume is 512 cm³, so:
   \[
   s^3 = 512
   \]
   Taking the cube root of both sides:
   \[
   s = \sqrt[3]{512} = 8 \, \text{cm}
   \]

3. **Surface Area of the Cube:**
   The surface area \( A \) of a cube is given by:
   \[
   A = 6s^2
   \]
   Substituting \( s = 8 \, \text{cm} \):
   \[
   A = 6 \times 8^2 = 6 \times 64 = 384 \, \text{cm}^2
   \]

### Answer:
The surface area of the cube is \( \boxed{384 \, \text{cm}^2} \), so the correct option is **D**.

---

Do you have any questions or need further explanation?

Here are 5 related questions you can explore:
1. What is the surface area of a cube with a volume of 729 cm³?
2. How do you find the diagonal of a cube if you know its side length?
3. What is the relationship between volume and surface area in different 3D shapes?
4. How do the surface areas of different shapes compare for the same volume?
5. How can the surface area of a sphere be calculated if its volume is known?

**Tip:** When dealing with cubes, remember that the volume grows with the cube of the side length, while the surface area grows with the square of the side length.

Tentukan luas permukaan kubus yang mempunyai volume 512 cm³!

This problem asks to calculate the surface area of a cube with a volume of 512 cm³. Using the cube root theorem and key geometric formulas, this step-by-step solution guides students through the process of solving for the surface area. Perfect for middle school students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation