If a cube's side is doubled, how does its volume change?

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Question: If a cube\'s side is doubled, how does its volume change?

Options:

Correct Answer: increases eightfold

Solution:

If the side is doubled, the new volume is (2s)³ = 8s³, which is eight times the original volume.

If a cube's side is doubled, how does its volume change?

If a cube's side is doubled, how does its volume change?

Step 1: Understand that the volume of a cube is calculated using the formula V = s³, where s is the length of one side of the cube.
Step 2: If the side of the cube is doubled, the new side length becomes 2s.
Step 3: Calculate the new volume using the new side length: V = (2s)³.
Step 4: Expand the calculation: (2s)³ = 2³ * s³ = 8 * s³.
Step 5: Compare the new volume (8s³) to the original volume (s³).
Step 6: Conclude that the new volume is 8 times the original volume.

Volume of a Cube – The volume of a cube is calculated using the formula V = s³, where s is the length of a side.
Scaling Properties – When the dimensions of a geometric shape are scaled, the volume changes by the cube of the scaling factor.