Math Problem Statement

What is the volume in cubic units?

Solution

The image shows a cube divided into smaller unit cubes. To find the volume of this larger cube in cubic units, we need to determine how many smaller cubes fit inside it.

Each side of the larger cube is composed of 4 smaller unit cubes. The volume of a cube is calculated using the formula:

Volume=side length3\text{Volume} = \text{side length}^3

Here, the side length is 4 units, so the volume is:

Volume=43=64 cubic units\text{Volume} = 4^3 = 64 \text{ cubic units}

Thus, the volume of the cube is 64 cubic units.

Would you like any further explanation on this? Here are five related questions you might want to explore:

  1. What would the volume be if the side length were doubled?
  2. How do you calculate the surface area of the cube shown in the image?
  3. What is the formula for the volume of a rectangular prism, and how does it relate to a cube?
  4. How many smaller cubes would fit inside the larger cube if each smaller cube had a different size?
  5. How would the volume change if the cube were stretched into a rectangular prism?

Tip: Always remember that volume scales by the cube of the side length. Doubling the side length increases the volume by eight times!

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Math Problem Analysis

Mathematical Concepts

Volume Calculation
Cubic Units
Geometry

Formulas

Volume of a Cube = side length^3

Theorems

Cube Volume Theorem

Suitable Grade Level

Grades 4-6