Math Problem Statement

The volume (V) of a cube can be determined when the length of each side (s) is known, using the formula below. Find the volume of a cube when: V = s3 ; s = 4 inches

Solution

To find the volume of the cube, we will use the formula:

V=s3V = s^3

where:

  • VV is the volume of the cube.
  • ss is the length of a side of the cube.

Given that s=4s = 4 inches, we can substitute this value into the formula:

V=43=4×4×4=64cubic inchesV = 4^3 = 4 \times 4 \times 4 = 64 \, \text{cubic inches}

So, the volume of the cube is 64 cubic inches.

Would you like further clarification or help with another problem? Here are a few related questions to explore:

  1. How do you calculate the surface area of a cube?
  2. What would the volume be if the side length was doubled to 8 inches?
  3. How is the volume formula for a cube derived from the formula for the volume of a rectangular prism?
  4. If a cube has a volume of 125 cubic inches, what is the length of each side?
  5. Can the formula for the volume of a cube be applied to other shapes? Why or why not?

Tip: To verify your calculations for the volume of a cube, always check if the side length is correctly cubed and double-check units for consistency.

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Math Problem Analysis

Mathematical Concepts

Geometry
Volume
Cube
Exponents

Formulas

V = s^3

Theorems

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Suitable Grade Level

Grades 5-7