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If the length of a side of a cube is doubled, how does its volume change?

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Question: If the length of a side of a cube is doubled, how does its volume change?

Options:

  1. Increases by 2 times
  2. Increases by 4 times
  3. Increases by 8 times
  4. Remains the same

Correct Answer: Increases by 8 times

Solution: 

The volume of a cube is given by V = a³. If the side length a is doubled, the new volume is (2a)³ = 8a³, which is 8 times the original volume.

If the length of a side of a cube is doubled, how does its volume change?

Practice Questions

Q1
If the length of a side of a cube is doubled, how does its volume change?
  1. Increases by 2 times
  2. Increases by 4 times
  3. Increases by 8 times
  4. Remains the same

Questions & Step-by-Step Solutions

If the length of a side of a cube is doubled, how does its volume change?
Correct Answer: 8 times the original volume
  • Step 1: Understand that a cube has 6 equal square faces and all sides are the same length.
  • Step 2: Know the formula for the volume of a cube, which is V = a³, where 'a' is the length of one side.
  • Step 3: If the side length 'a' is doubled, the new side length becomes 2a.
  • Step 4: Substitute the new side length into the volume formula: V = (2a)³.
  • Step 5: Calculate (2a)³, which means (2a) * (2a) * (2a).
  • Step 6: This simplifies to 2 * 2 * 2 * a * a * a = 8a³.
  • Step 7: Compare the new volume (8a³) to the original volume (a³).
  • Step 8: Conclude that the new volume is 8 times the original volume.
  • Volume of a Cube – Understanding the formula for the volume of a cube (V = a³) and how changes in side length affect volume.
  • Exponential Growth – Recognizing that doubling a linear dimension results in an exponential increase in volume.
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