Math Problem Statement

What is the surface area of this cube?

Solution

The cube shown in the image has each side measuring 6 cm. The surface area of a cube is calculated using the formula 6s26s^2, where ss is the length of one side.

Here, each side of the cube is 6 cm, so:

Surface Area=6×(6 cm)2=6×36 cm2=216 cm2\text{Surface Area} = 6 \times (6 \text{ cm})^2 = 6 \times 36 \text{ cm}^2 = 216 \text{ cm}^2

Therefore, the surface area of the cube is 216 square centimeters.

Would you like to explore further details or have any questions about this calculation? Here are some follow-up questions you might consider:

  1. What is the volume of this cube?
  2. How does the surface area change if the side length doubles?
  3. What would be the surface area if the shape were a rectangular prism with the same height as this cube but different length and width?
  4. Can you calculate the diagonal of this cube?
  5. How would the calculations differ if this were a sphere with a diameter of 6 cm?

Tip: Always ensure to square the length of the side correctly when computing the area of a face in cubic structures.

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Math Problem Analysis

Mathematical Concepts

Geometry
Surface Area Calculation

Formulas

Surface area of a cube = 6s^2

Theorems

Basic Geometric Properties of a Cube

Suitable Grade Level

Grades 6-8