Question

If the edge of a cube is doubled then the total surface area will become how many times of the previous total surface area?

• A. Two times
• B. Four times
• C. Six times
• D. Twelve times

Hint:

When a linear dimension (like edge, radius) is scaled by a factor of \(k\), the area is scaled by a factor of \(k^2\), and the volume is scaled by a factor of \(k^3\). Here, the edge is doubled (\(k=2\)), so the area becomes \(2^2 = 4\) times larger.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
The total surface area (TSA) of a cube depends on the square of its edge length. We need to see how the TSA changes when the edge length is doubled.

Step 2: Key Formula or Approach:
The formula for the total surface area of a cube with edge length \(a\) is:
\[ TSA = 6a^2 \]

Step 3: Detailed Explanation:
Let the original edge length be \(a\). The original TSA is \(TSA_{original} = 6a^2\).
Now, the edge is doubled. The new edge length is \(a_{new} = 2a\).
Let's calculate the new total surface area with this new edge:
\[ TSA_{new} = 6(a_{new})^2 = 6(2a)^2 \] \[ TSA_{new} = 6(4a^2) = 4 \times (6a^2) \] Since \(6a^2 = TSA_{original}\), we have:
\[ TSA_{new} = 4 \times TSA_{original} \] This means the new total surface area is four times the original total surface area.

Step 4: Final Answer:
The total surface area will become Four times the previous total surface area.