Question

A cube has side length doubled. Its volume becomes:

• A. Twice
• B. Four times
• C. Six times
• D. Eight times

Hint:

For any 3D shape, if all linear dimensions are scaled by a factor \( k \), the volume is scaled by \( k^3 \) and the surface area by \( k^2 \).

Answer 1

The Correct Option is D

Step 1: Understanding the Question:
We need to find the factor by which the volume of a cube increases when its side length is doubled.

Step 2: Key Formula or Approach:
The volume \( V \) of a cube with side length \( s \) is given by: \[ V = s^3 \]

Step 3: Detailed Explanation:
Let the initial side be \( s_1 \). The initial volume is \( V_1 = s_1^3 \).
If the side length is doubled, the new side \( s_2 = 2s_1 \).
The new volume \( V_2 \) will be: \[ V_2 = (s_2)^3 = (2s_1)^3 \] \[ V_2 = 8 \cdot s_1^3 \] Since \( V_1 = s_1^3 \), we have: \[ V_2 = 8 \cdot V_1 \]

Step 4: Final Answer:
The volume becomes eight times the original volume.