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

₹0.0

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

Options:

Correct Answer: Increases by 8 times

Solution:

Volume of a cube is given by V = a³. If a is doubled, V becomes (2a)³ = 8a³, hence volume increases by 8 times.

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

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

Step 1: Understand that a cube has sides of equal length. Let's call the length of one side 'a'.
Step 2: The formula for the volume of a cube is V = a³, which means you multiply the length of the side by itself three times.
Step 3: If we double the length of the side, the new length becomes 2a.
Step 4: Now, we need to find the new volume using the new side length. The new volume is V = (2a)³.
Step 5: Calculate (2a)³. This means (2a) * (2a) * (2a).
Step 6: When you multiply it out, you get 2 * 2 * 2 * a * a * a = 8a³.
Step 7: Compare the new volume (8a³) to the original volume (a³).
Step 8: Since 8a³ is 8 times a³, we conclude that the volume increases by 8 times.

Volume of a Cube – Understanding the formula for the volume of a cube (V = a³) and how changes in the side length affect the volume.
Exponential Growth – Recognizing that doubling a linear dimension results in an exponential increase in volume.