https://file.aiquickdraw.com/mathbot/file/1726695453745e4674y53.jpg

The problem asks to calculate the volume of a cube using exponents, and the diagram shows a large cube decomposing into smaller cubes. To solve this:

1. **Step 1: Identify the dimensions of the cube.**
   The large cube appears to be divided into smaller cubes. Each row and layer consists of **3 small cubes**. Therefore, the side length of the large cube is \(3\) units.

2. **Step 2: Use the volume formula for a cube.**
   The volume \(V\) of a cube is calculated using the formula:

   \[
   V = s^3
   \]
   where \(s\) is the side length of the cube.

3. **Step 3: Calculate the volume.**
   Since the side length \(s = 3\), the volume is:

   \[
   V = 3^3 = 3 \times 3 \times 3 = 27 \, \text{cubic units}
   \]

Thus, the volume of the cube is **27 cubic units**.

Would you like more details on this? Here are 5 related questions:

1. How do exponents relate to calculating the volume of a cube?
2. What happens to the volume when you double the side length of a cube?
3. How would the volume change if each smaller cube had a side length of 1 unit instead?
4. Can you apply the same exponent rule to other 3D shapes like a rectangular prism?
5. How does decomposing the cube into smaller parts help in visualizing its volume?

**Tip**: Always remember that the volume of any cube is simply the cube of its side length!

Calculate the volume of the cube. (Hint: How can you use exponents? Decompose?)

Learn how to calculate the volume of a cube using exponents. This problem breaks down the steps to decompose the cube and apply the volume formula (V = s^3). Suitable for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation