Math problem set Grade 9 Science

Elmcrest Storage Tank: Fire Flow, Reserve, and Volume

A grade 9 problem set where students model a fictional town's cylindrical tank, find its volume in gallons, and track how much water a two-hour fire flow draws down.

Grade: Grade 9
Subject: Science
Material: Math problem set
Time: 45 min
Prep: No prep
Materials: Calculator

Standards

HSG-MG.A.1 Common Core Math

Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).

How this material aligns: Problem 1 models the Elmcrest storage tank as a cylinder and uses the 0.785 times diameter-squared times depth formula to estimate its capacity, the shape-to-real-object modeling this standard targets.

All materials for HSG-MG.A.1 →

HSN-Q.A.1 Common Core Math

Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.

How this material aligns: Problems 2 through 9 carry cubic feet, gallons, gallons per minute, and minutes through volume, fire-flow, and reserve calculations while keeping units consistent across the multi-step draw-down.

All materials for HSN-Q.A.1 →

HS-ETS1-3 NGSS

Evaluate a solution to a complex real-world problem based on prioritized criteria and trade-offs that account for a range of constraints, including cost, safety, reliability, and aesthetics as well as possible social, cultural, and environmental impacts.

How this material aligns: Items 5 through 7 test whether the tank still meets its fire-flow and reserve requirements after a two-hour fire, and item 10 weighs the pressure trade-off between a tall narrow tank and a short wide one.

All materials for HS-ETS1-3 →

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This material is in the public domain (CC0) and may be copied, edited, and shared freely, without attribution. Updated 2026-07-23.

Objectives

Students will model a storage tank as a cylinder and calculate its volume in cubic feet and gallons.
Students will use fire-flow and demand rates to find how much water a tank supplies during a fire and how much remains.

Vocabulary

Key words: cylinder, fire flow, reserve, storage tank, demand

Teacher overview

A town's storage tank has to do two jobs at once during a fire: keep supplying everyday demand and deliver a large extra flow to the hydrants. This set has students size a cylindrical tank, then track how a two-hour fire draws it down and whether it stays above its required reserve. The tank is modeled with the standard capacity formula, volume equals 0.785 times the diameter squared times the depth. A common misconception is to plug the radius into that formula; the 0.785 factor already expects the full diameter, so using the radius cuts the calculated volume to a quarter of its true value.

Elmcrest Storage Tank: Fire Flow, Reserve, and Volume — Grade 9 Science

Name: ____________________________ Date: ______________

Problems

Use these facts about the Elmcrest storage tank in the town of Elmcrest, a fictional community, for every problem.

The tank is a cylinder 50 ft in diameter with a water depth of 30 ft.
Volume (cu ft) = 0.785 x diameter^2 x depth.
One cubic foot holds 7.48 gallons.
Fire code requires a fire flow of 1,500 gpm for 2 hours, on top of the normal demand.
Normal demand during the fire is 350 gpm.
The tank starts completely full.

Model the tank as a cylinder and find its volume in cubic feet.
Convert the tank's volume to gallons.
During a fire, the tank supplies the 1,500 gpm fire flow plus the 350 gpm normal demand. What is the total draw rate, in gpm?
How many gallons does the tank supply during the full 2-hour (120-minute) fire at that total draw rate?
What percent of the full tank does the fire draw in problem 4 use? Round to the nearest whole percent.
If nothing refills the tank during the fire, how many gallons remain when the fire ends?
Fire code requires the tank to keep at least 25 percent of its full volume in reserve at all times. Is the remaining volume from problem 6 above or below that reserve, and by how many gallons?
Now suppose the fill pump runs during the fire, adding 700 gpm. What is the net rate at which the tank drains, in gpm (draw minus fill)?
With the pump running, how many gallons does the tank lose over the 2-hour fire?
Explain why a tall, narrow tank and a short, wide tank can hold the same volume, using the cylinder formula, and why a utility might still prefer the taller tank for delivering pressure.

From Water for Schools (waterforschools.org). This material is in the public domain (CC0) and may be copied, edited, and shared freely.

Answer Key

Answer: 58,875 cu ft. Volume = 0.785 x 50^2 x 30 = 0.785 x 2,500 x 30 = 58,875 cubic feet.
Answer: 440,385 gallons. 58,875 cu ft x 7.48 gal/cu ft = 440,385 gallons.
Answer: 1,850 gpm. 1,500 gpm fire flow + 350 gpm normal demand = 1,850 gpm total draw.
Answer: 222,000 gallons. 1,850 gpm x 120 minutes = 222,000 gallons drawn during the fire.
Answer: 50 percent. 222,000 / 440,385 = 0.504, which rounds to 50 percent of the full tank.
Answer: 218,385 gallons. 440,385 - 222,000 = 218,385 gallons remain.
Answer: Above, by 108,289 gallons. The reserve is 25 percent of 440,385 = 110,096 gallons; the remaining 218,385 gallons is above it by 218,385 - 110,096 = 108,289 gallons.
Answer: 1,150 gpm. Net drain = 1,850 gpm draw - 700 gpm fill = 1,150 gpm.
Answer: 138,000 gallons. 1,150 gpm x 120 minutes = 138,000 gallons lost over the fire, less than without the pump because the fill offsets part of the draw.
Answer: Volume depends on the diameter squared times the depth, so a tank can trade width for height and keep the same product. For example, a wider tank with less depth and a narrower tank with more depth can match. A utility may still prefer the taller tank because the extra height of water raises the pressure it can deliver to the system, since pressure depends on the height of water above the customer.

Differentiation

Support

Provide a labeled cylinder diagram marking the diameter and depth, and give students the value of the diameter squared (2,500) already computed so they can focus on the volume and conversion steps. Allow a calculator throughout.

Extension

Ask students to find the diameter a tank would need to hold the same 440,385 gallons at a depth of only 20 feet, and to comment on the trade-off between a shorter, wider tank and the original taller one.

ELL supports

Pre-teach "diameter" and "reserve" (water kept back for emergencies) with a labeled picture of a tank and a marked reserve line. Allow problem 10 to be answered with a labeled sketch of two tanks plus a short sentence.

Extensions

Have students find the diameter and height of a real water tank in their community, estimate its water depth, and calculate its capacity in gallons, then compare that capacity with the fire-flow demand their local fire code would require for a two-hour fire.