If the length of a side of a cube is doubled, how does its volume change?
Practice Questions
1 question
Q1
If the length of a side of a cube is doubled, how does its volume change?
Increases by 2 times
Increases by 4 times
Increases by 8 times
Remains the same
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.
Questions & Step-by-step Solutions
1 item
Q
Q: If the length of a side of a cube is doubled, how does its volume change?
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.
Steps: 8
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.
