Question

1. if you double each edge of a cube, how many times larger is the volume? $v = s^3$

Explanation:

Step1: Define original cube volume

Let original edge length be $s$. Original volume: $V_1 = s^3$

Step2: Define new cube edge length

Doubled edge length: $2s$

Step3: Calculate new cube volume

New volume: $V_2 = (2s)^3 = 8s^3$

Step4: Find volume ratio

Ratio of new to original: $\frac{V_2}{V_1} = \frac{8s^3}{s^3} = 8$

Answer:

The volume is 8 times larger.