Math Problem Statement

What is the volume, in cubic inches, of a cube with an edge length of 12 inches?

Solution

The volume VV of a cube is given by the formula:

V=s3V = s^3

where ss is the length of an edge of the cube.

Given that the edge length is s=12s = 12 inches, we can calculate the volume:

V=123=12×12×12=1,728cubic inchesV = 12^3 = 12 \times 12 \times 12 = 1,728 \, \text{cubic inches}

So, the volume of the cube is 1,728 cubic inches.

Would you like more details or have any further questions?

Here are 5 related questions to deepen your understanding:

  1. What is the surface area of a cube with an edge length of 12 inches?
  2. How does the volume of a cube change if the edge length is doubled?
  3. If the volume of a cube is 8,000 cubic inches, what is the edge length of the cube?
  4. What is the volume of a rectangular prism with dimensions 12 inches by 12 inches by 12 inches?
  5. How would you calculate the diagonal of a cube with a given edge length?

Tip: When scaling the edge length of a cube, the volume changes by the cube of the scaling factor!

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Math Problem Analysis

Mathematical Concepts

Geometry
Volume of a Cube
Exponents

Formulas

Volume of a cube: V = s^3

Theorems

Cube volume scaling theorem

Suitable Grade Level

Grades 6-8