13.3 Volume (7.5 gal/ft³), Weight (62.5 lb/ft³) & Flow Comparisons

13.3 Volume (7.5 gal/ft³), Weight (62.5 lb/ft³) & Flow Comparisons

Quick Answer: Gallons in a tank = (L × W × H in feet) × 7.5. Weight of water = (L × W × H) × 62.5. Water flowed = gpm × minutes. Packet scene total: E1 1,000 + E2 4,000 + L3 20,000 = 25,000 gallons. E1 is 25% of E2; E1+E2 is 20% of total (TRUE).

The last block of Section Twelve gives two physical constants, then asks you to size tanks and compare multi-company water use. Nothing here requires advanced geometry—only rectangular volume, multiply by a constant, and percent comparisons of flow totals.

Given constants (memorize exactly)

The packet states (paraphrased for study):

Do not mix them. Gallons questions → 7.5. Weight questions → 62.5. Using the wrong constant is the most common full-point loss on these items.

Method 1 — Rectangular tank volume

Formula

Volume (ft³) = length (ft) × width (ft) × height (ft)

All three dimensions must be in feet. If a problem ever gave inches, convert first (12 in = 1 ft). The packet examples are already in feet.

Then convert volume to gallons or weight

Gallons = volume_ft³ × 7.5
Weight_lb = volume_ft³ × 62.5

Worked example — gallons capacity (packet Q6)

Given: Rectangular water tank 4 ft × 4 ft × 1 ft high.

Find: Gallons at capacity.

Work:

Volume = 4 × 4 × 1 = 16 ft³
Gallons = 16 × 7.5 = 120 gallons

Answer: 120 gallons.

Why other choices fail

Sanity check: A small 4×4×1 tank is only 16 cubic feet—120 gallons is a modest booster-size volume, not thousands of gallons. Huge answers like 7,500 should make you re-check the constant.

Worked example — water weight (packet Q7)

Given: Rectangular tank 10 ft × 4 ft × 2.5 ft high, filled.

Find: Weight of the water (pounds).

Work:

Volume = 10 × 4 × 2.5 = 100 ft³
Weight = 100 × 62.5 = 6,250 pounds

Answer: 6,250 pounds.

Arithmetic note on 2.5

10 × 4 = 40; 40 × 2.5 = 40 × 2 + 40 × 0.5 = 80 + 20 = 100. Then 100 × 62.5:

100 × 62 = 6,200
100 × 0.5 = 50
Total = 6,250

Or: 62.5 × 100 = 6,250 directly.

Distractors

If you used 7.5 by mistake: 100 × 7.5 = 750 gallons—a valid gallon answer for this tank, but not what Q7 asks. Read “weighs” vs “gallons” every time.

Combined reference table (both constants)

Method 2 — Flow totals (gpm × time)

Formula per apparatus

Gallons from one unit = flow rate (gpm) × time (minutes)

Hose lengths do not enter the gallon total unless the question asks about hose amount. For packet Q8, hose is context; water total uses gpm and minutes only.

Hose sections note (packet context)

The packet notes that each hose used was comprised of 50-ft sections. That matters if a question asks how many sections were used:

Number of 50-ft sections = total hose feet ÷ 50

Examples from the December 20, 2001 strip-mall scenario:

You may need section counts for comparison statements about hose; you do not need them for total gallons in Q8.

Worked example — multi-apparatus water total (packet Q8)

Given (strip mall fire):

Find: Total gallons pumped by all apparatus.

Work:

Engine 1: 100 gpm × 10 min = 1,000 gallons
Engine 2: 200 gpm × 20 min = 4,000 gallons
Ladder 3: 1,000 gpm × 20 min = 20,000 gallons
────────────────────────────────────────────
Total: 1,000 + 4,000 + 20,000 = 25,000 gallons

Answer: 25,000 gallons.

Distractors

Method 3 — Comparative / percent statements (packet Q9–Q10)

After you have each unit’s gallons, test statements by computing actual percents or multiples—do not “eyeball” the story.

Per-unit gallons (from above)

Packet Q9 — which statement is most accurate?

Evaluate each option:

A. “Engine 1 pumped approximately 50% longer on the fire than Engine 2.”
Times: E1 = 10 min, E2 = 20 min. E1 ran half as long, not 50% longer. False.

B. “Engines 1 & 2 combined pumped approximately 40% of total water.”
E1+E2 = 5,000; 5,000 ÷ 25,000 = 20%, not 40%. False.

C. “Ladder 3 used approximately 50% more hose than Engines 1 & 2 combined.”
L3 hose = 500 ft. E1+E2 hose = 150 + 200 = 350 ft.
50% more than 350 would be 350 × 1.5 = 525 ft. Ladder used 500 ft—close but the option says “approximately 50% more”; more precise comparison: 500 / 350 ≈ 1.43 (about 43% more), not a clean “50% more.” The packet’s most accurate choice is D, which matches exactly.

D. “Engine 1 supplied approximately 25% of the water on the fire compared to that water supplied by Engine 2.”
E1 ÷ E2 = 1,000 ÷ 4,000 = 0.25 = 25%. True / most accurate.

Answer: D.

Packet Q10 — True or False

Statement: The amount of water flowed by Engine 1 and Engine 2 combined was approximately 20% of total water flowed.

E1 + E2 = 5,000
Total = 25,000
5,000 ÷ 25,000 = 0.20 = 20%

Answer: TRUE.

Comparison toolkit (use on any similar item)

Full scene summary card

Exam workflow for 13.3

1. Tank problem? Compute ft³ first; then ×7.5 (gallons) or ×62.5 (pounds)—match the verb in the question.
2. Flow problem? For each unit: gpm × minutes; then sum. Ignore hose feet unless asked about hose or sections.
3. True/false or “most accurate”? Calculate each claim; pick the one that matches the arithmetic, not the one that “sounds right.”
4. Sections of hose? Divide total feet by 50.

Master the two constants and the gpm×time product, and the entire packet math block is mechanical—then use the same habits on aptitude-style variants with new numbers.