Question

1. how do you see it? package a is a cube with a volume of 500 cubic inches. package b is a cube with a volume of 250 cubic inches. is the length x of a side of package a greater than, less than, or equal to twice the length of a side of package b? explain.

Explanation:

Step1: Find side - length formula for a cube

The volume formula for a cube is $V = s^{3}$, where $V$ is the volume and $s$ is the side - length. So, $s=\sqrt[3]{V}$.

Step2: Calculate the side - length of package A

Let the side - length of package A be $x_A$. Given $V_A = 500$ cubic inches, then $x_A=\sqrt[3]{500}$.

Step3: Calculate the side - length of package B

Let the side - length of package B be $x_B$. Given $V_B = 250$ cubic inches, then $x_B=\sqrt[3]{250}$.

Step4: Compare $x_A$ and $2x_B$

We want to check if $x_A>2x_B$, $x_A < 2x_B$ or $x_A=2x_B$. Calculate $2x_B = 2\sqrt[3]{250}=\sqrt[3]{2^{3}\times250}=\sqrt[3]{2000}$.
Since $\sqrt[3]{500}<\sqrt[3]{2000}$, we have $x_A<2x_B$.

Answer:

The length of a side of package A is less than twice the length of a side of package B.