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.
