Question

What will be the change in the volume of a cube when its side becomes 10 times the original side?

• A. Volume becomes 1000 times
• B. Volume becomes 10 times
• C. Volume becomes 100 times
• D. Volume becomes \( \frac{1}{1000} \) times

Hint:

For 3D shapes, if the dimension changes by a factor of \( k \), the volume changes by \( k^3 \).

Answer 1

The Correct Option is A

Step 1: Formula for volume of a cube
The volume \( V \) of a cube is given by: \[ V = s^3 \] where \( s \) is the side length.
Step 2: Finding the new volume
If the side length becomes 10 times, then the new volume: \[ V' = (10s)^3 = 1000s^3 \] Thus, the volume increases 1000 times.