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

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

Options:

Correct Answer: It increases eightfold

Solution:

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

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

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

Step 1: Understand that a cube has equal length, width, and height. Let's call the original length 's'.
Step 2: Calculate the original volume of the cube using the formula for volume: V = s³.
Step 3: If the length of the cube is doubled, the new length becomes '2s'.
Step 4: Calculate the new volume using the new length: V = (2s)³.
Step 5: Simplify the new volume: (2s)³ = 2³ * s³ = 8s³.
Step 6: Compare the new volume (8s³) to the original volume (s³).
Step 7: 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.
Effect of Scaling – Doubling the side length of a cube results in a volume increase by a factor of 2³, which is 8.