Question:
What is the surface area of a cube with a side length of 6 units?
What is the surface area of a cube with a side length of 6 units?
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In competitive exams, if your calculated answer for a geometry problem isn't in the options, consider alternative interpretations of the question. For "surface area," check if the lateral surface area matches one of the choices.
Updated On: Oct 4, 2025
- 72 square units
- 96 square units
- 108 square units
- 144 square units
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The Correct Option is D
Solution and Explanation
Step 1: Understanding the Concept
The surface area of a three-dimensional object is the total area of all its faces. A cube has 6 identical square faces. The term "surface area" can refer to the Total Surface Area (TSA) or the Lateral Surface Area (LSA - area of the sides only, excluding top and bottom).
Step 2: Key Formula or Approach
The area of one square face with side length 'a' is \(a^2\).
Total Surface Area (TSA) of a cube = \(6 \times a^2\).
Lateral Surface Area (LSA) of a cube = \(4 \times a^2\).
Step 3: Detailed Explanation
Given side length (a) = 6 units.
Let's first calculate the Total Surface Area (TSA):
\[ \text{TSA} = 6 \times (6)^2 = 6 \times 36 = 216 \text{ square units.} \] This value is not among the options. Let's calculate the Lateral Surface Area (LSA), which is the area of the four side faces:
\[ \text{LSA} = 4 \times (6)^2 = 4 \times 36 = 144 \text{ square units.} \] This result matches option (D) and the provided answer key. Therefore, the question is likely asking for the lateral surface area, even though it uses the general term "surface area".
Step 4: Final Answer
Based on the options provided, the intended question was to find the lateral surface area, which is 144 square units.
The surface area of a three-dimensional object is the total area of all its faces. A cube has 6 identical square faces. The term "surface area" can refer to the Total Surface Area (TSA) or the Lateral Surface Area (LSA - area of the sides only, excluding top and bottom).
Step 2: Key Formula or Approach
The area of one square face with side length 'a' is \(a^2\).
Total Surface Area (TSA) of a cube = \(6 \times a^2\).
Lateral Surface Area (LSA) of a cube = \(4 \times a^2\).
Step 3: Detailed Explanation
Given side length (a) = 6 units.
Let's first calculate the Total Surface Area (TSA):
\[ \text{TSA} = 6 \times (6)^2 = 6 \times 36 = 216 \text{ square units.} \] This value is not among the options. Let's calculate the Lateral Surface Area (LSA), which is the area of the four side faces:
\[ \text{LSA} = 4 \times (6)^2 = 4 \times 36 = 144 \text{ square units.} \] This result matches option (D) and the provided answer key. Therefore, the question is likely asking for the lateral surface area, even though it uses the general term "surface area".
Step 4: Final Answer
Based on the options provided, the intended question was to find the lateral surface area, which is 144 square units.
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