Question

1. it takes 8 cubic inches of water to fill a cube. if each edge of the cube is doubled, how much water is needed to fill the new cube? $v = s^3$

Explanation:

Step1: Find original edge length

The volume formula of a cube is $V = s^3$. Given $V=8$, solve for $s$:
$$s = \sqrt[3]{V} = \sqrt[3]{8} = 2$$

Step2: Calculate new edge length

Double the original edge length:
$$s_{\text{new}} = 2 \times 2 = 4$$

Step3: Compute new cube volume

Use the volume formula for the new cube:
$$V_{\text{new}} = s_{\text{new}}^3 = 4^3 = 64$$

Answer:

64 cubic inches