Math Problem Statement

Each edge of a Rubik's cube has a length of about 14 cm. What is the volume of the Rubik's cube?

Solution

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"a) Each edge of a Rubik's cube has a length of about 14 cm. What is the volume of the Rubik's cube?"

Solution:

To find the volume of a cube, we use the formula for the volume of a cube:

V=s3V = s^3

Where VV is the volume and ss is the length of an edge of the cube.

Given that the edge of the Rubik's cube is s=14cms = 14 \, \text{cm}, the volume can be calculated as:

V=143=14×14×14=2744cm3V = 14^3 = 14 \times 14 \times 14 = 2744 \, \text{cm}^3

Thus, the volume of the Rubik's cube is 2744cm32744 \, \text{cm}^3.

Would you like further details or have any questions?

Here are some follow-up questions to expand your understanding:

  1. What is the surface area of the same Rubik's cube?
  2. How would the volume change if the edge length doubled?
  3. What is the formula for the surface area of a cube?
  4. Can you calculate the volume if the edge length is given in meters?
  5. How does the volume of a cube scale with respect to its edge length?

Tip: Always remember that the volume of a cube increases exponentially as the edge length increases, since it's proportional to the cube of the edge length.

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Math Problem Analysis

Mathematical Concepts

Geometry
Volume of Cube

Formulas

Volume of a cube V = s^3, where s is the length of an edge

Theorems

Geometric properties of a cube

Suitable Grade Level

Grades 6-8