 In August 2017, Hurricane Harvey dumped more water on Houston, TX than the
western half of the United States sees all year [1]. The total amount of water dumped by
Harvey over Texas, Louisiana, Tennessee, and Kentucky was estimated at 33 trillion gallons
[2]. One trillion is 1 × 1012.
EGR 1301 – Introduction to Engineering
a. If this volume of water were collected into a cube, how long would each side of the
cube be in km? Show your work.


We are tasked with finding the side length of a cube that could hold 33 trillion gallons of water.

### Step 1: Convert gallons to cubic kilometers
First, we need to convert the volume of water from gallons to cubic kilometers because we want the side length of the cube in kilometers.

1 gallon = 3.78541 liters = \( 3.78541 \times 10^{-3} \) cubic meters (m³)

1 cubic meter = \( 1 \times 10^{-9} \) cubic kilometers (km³)

Thus, 1 gallon = \( 3.78541 \times 10^{-12} \) km³.

Now, the total amount of water is 33 trillion gallons, which is:

\[
33 \times 10^{12} \text{ gallons}
\]

Convert this to cubic kilometers:

\[
33 \times 10^{12} \text{ gallons} \times 3.78541 \times 10^{-12} \text{ km³/gallon} = 124.91853 \text{ km³}
\]

### Step 2: Find the side length of the cube
The volume \( V \) of a cube is given by:

\[
V = s^3
\]

Where \( s \) is the side length of the cube and \( V \) is the volume of the cube. We now know that the volume \( V = 124.91853 \text{ km³} \).

To find the side length \( s \), take the cube root of the volume:

\[
s = \sqrt[3]{V} = \sqrt[3]{124.91853} \text{ km}
\]

Let’s calculate that.

\[
s \approx 5.01 \text{ km}
\]

### Final Answer:
Each side of the cube would be approximately **5.01 km** long.

---

Would you like further details or have any questions? Here are 5 related questions for you:

1. How does the volume of this cube compare to the volume of famous lakes or oceans?
2. How much would this volume of water weigh?
3. What is the significance of converting to cubic kilometers rather than staying in gallons?
4. How would the side length change if the volume was doubled?
5. Can this method be used to calculate the volume of irregularly shaped objects?

**Tip:** For accurate unit conversions, always double-check the conversion factors, especially when working with large-scale units like cubic kilometers or trillions of gallons.

In August 2017, Hurricane Harvey dumped more water on Houston, TX than the western half of the United States sees all year. The total amount of water dumped by Harvey over Texas, Louisiana, Tennessee, and Kentucky was estimated at 33 trillion gallons. One trillion is 1 × 10^12. If this volume of water were collected into a cube, how long would each side of the cube be in km?

Explore how to calculate the side length of a cube that could hold 33 trillion gallons of water. This problem covers essential math concepts such as volume conversion, cube root calculation, and unit conversions from gallons to cubic kilometers. Suitable for students in Grades 10-12.

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