Math  /  Numbers & Operations

QuestionUse the table, along with dimensional analysis, to convert the given unit to the unit indicated. 20,000ft3 to gal 20,000 \mathrm{ft}^{3} \text { to gal } \begin{tabular}{|ll|} \hline \multicolumn{1}{|c|}{2 pints ( pt))} & =1=1 quart ( qt)) \\ \hline 4 quarts & =1=1 gallon (gal) \\ \hline 1 gallon & =128=128 ounces (oz)(\mathrm{oz}) \\ \hline 1 cup (c) & =8=8 ounces \\ \hline Volume in Cubic Units & Capacity \\ \hline 1 cubic yard & about 200 gallons \\ \hline 1 cubic foot & about 7.48 gallons \\ \hline 231 cubic inches & about 1 gallon \\ \hline \end{tabular} \square gal (Round to the nearest hundredth as needed.)

Studdy Solution

STEP 1

What is this asking? We need to convert a volume from cubic feet to gallons. Watch out! Make sure to use the correct conversion factor and watch your units!

STEP 2

1. Find the conversion factor.
2. Perform the conversion.

STEP 3

Alright, let's **dive in**!
We're given a super helpful table, and it tells us that 11 cubic foot is about 7.487.48 gallons.
This is our **golden ticket**, our **conversion factor**!

STEP 4

We're starting with 20,00020,000 ft3\text{ft}^3.
We want to **transform** this into gallons.
Since 1 ft37.48 gal1 \text{ ft}^3 \approx 7.48 \text{ gal}, we can **multiply** our starting value by this conversion factor.
This is like saying "for every one cubic foot, we have about 7.487.48 gallons".

STEP 5

Let's **do the math**: 20,000 ft37.48 gal1 ft320,000 \text{ ft}^3 \cdot \frac{7.48 \text{ gal}}{1 \text{ ft}^3}

STEP 6

Notice how the ft3\text{ft}^3 units **divide to one**, leaving us with just gallons.
This is exactly what we want!
Now, we just need to **multiply** the numbers: 20,0007.48=149,60020,000 \cdot 7.48 = 149,600

STEP 7

So, we have 149,600149,600 gallons.
Awesome!

STEP 8

149,600149,600 gal

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