Math Problem Statement

Find the surface area of the prism. The prism is a cube with side length 7 yards.

Solution

To solve this problem, we need to calculate the surface area of the given cube.

Steps to Solve:

  1. Cube Basics:

    • A cube has 6 identical square faces.
    • The surface area of a cube is given by: Surface Area=6×(side length)2\text{Surface Area} = 6 \times (\text{side length})^2
  2. Plugging in Values:

    • The side length of the cube is 7yd7 \, \text{yd}.
    • Substituting into the formula: Surface Area=6×(7)2\text{Surface Area} = 6 \times (7)^2
  3. Calculations:

    • (7)2=49(7)^2 = 49
    • 6×49=2946 \times 49 = 294

Final Answer:

The surface area of the cube is: 294yd2\boxed{294 \, \text{yd}^2}


Would you like a detailed explanation of how surface area relates to other prisms?
Here are five related questions for you to consider:

  1. How is the surface area formula different for a rectangular prism?
  2. What is the relationship between volume and surface area in a cube?
  3. How would the surface area change if the side length doubled?
  4. How do we calculate the surface area for non-cubical solids like cylinders?
  5. Why does a cube have the smallest surface area for a given volume compared to other shapes?

Tip: Always double-check whether a prism is a cube or rectangular, as it changes the calculations!

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Math Problem Analysis

Mathematical Concepts

Geometry
Surface Area of Prisms

Formulas

Surface Area of a Cube = 6 × (side length)^2

Theorems

Surface Area Calculation

Suitable Grade Level

Grades 6-8