Project Grade 8 Math

Sizing a Water Tower for Cottonwood Estates: A Volume and Cost Project

A four-session grade 8 project where teams size a cylindrical water tower, then use a system of equations to choose the cheaper of two suppliers within a fixed budget.

Grade: Grade 8
Subject: Math
Material: Project
Time: 4 sessions, ~200 min total
Prep: Moderate prep
Materials: Grid paper, Calculators, Printed supplier cost sheet (teacher-provided), Poster board or presentation software

Standards

8.G.C.9 Common Core Math

Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

How this material aligns: Teams calculate candidate cylindrical tank volumes in cubic feet and gallons during Milestone 2, applying the cylinder volume formula to a real design constraint exactly as this standard requires.

All materials for 8.G.C.9 →

8.EE.C.8 Common Core Math

Analyze and solve pairs of simultaneous linear equations, understanding that solutions correspond to points of intersection, and solving systems by graphing and algebraically in the context of real-world problems.

How this material aligns: Teams write and solve a system of two linear cost equations to find the break-even cubic footage between two suppliers during Milestone 3, the real-world systems application this standard targets.

All materials for 8.EE.C.8 →

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This material is in the public domain (CC0) and may be copied, edited, and shared freely, without attribution. Updated 2026-07-16.

Objectives

Students will calculate the volume of a cylindrical water tower in cubic feet and convert it to gallons.
Students will write and solve a system of two linear equations to find the break-even point between two cost structures.
Students will use volume and cost analysis to justify a final design recommendation within a stated budget.

Vocabulary

Key words: cylinder volume, system of equations, break-even point, budget constraint

Teacher overview

Cottonwood Estates (a fictional new subdivision used for this project) needs a recommendation for a new water tower, and the fictional Cottonwood Estates Water Board has asked student teams to size a tank and choose between two suppliers before a final budget decision. Over four sessions, teams calculate cylindrical tank volumes that meet a minimum storage requirement, compare two suppliers' cost structures using a system of linear equations, and present a final recommendation. A common misconception this project is built to correct is assuming that a larger tank is automatically the better choice; the project's fixed budget makes clear that more storage is not free, and teams must weigh volume against cost directly.

Sizing a Water Tower for Cottonwood Estates: A Volume and Cost Project — Grade 8 Math

Name: ____________________________ Date: ______________

Project Brief

Driving question: What size water tower should Cottonwood Estates build, and which supplier should build it?

Scenario: Cottonwood Estates is a fictional new subdivision. Its Water Board asked student teams to design a water tower. The board gave a minimum size, zoning limits, a budget, and two supplier price lists.

Constraints:

Minimum storage: the tank must hold at least 150,000 gallons.
Zoning limit: diameter cannot exceed 40 feet.
Zoning limit: height cannot exceed 50 feet.
Budget: the Water Board approved up to $210,000 for the tank.
Supplier A: $150,000 base cost, plus $2.50 per cubic foot of tank volume.
Supplier B: $90,000 base cost, plus $4.75 per cubic foot of tank volume.

Final deliverable: A labeled spec sheet. It shows the chosen diameter and height, plus the volume math. Teams also write a one-page proposal to the Water Board. The proposal names the supplier and explains why the design fits the budget and the storage rule.

Milestones

Session 1 — Research and constraints: Teams review the cylinder volume formula. Volume in cubic feet equals 0.785 times diameter squared times depth. Multiply by 7.48 to get gallons. Teams review all six items in the Constraints list above. As a warm-up, each team finds the volume, in gallons, of a sample tank 20 feet across and 30 feet deep. Output: a completed warm-up calculation, checked against the teacher's answer.
Session 2 — Draft two tank designs: Teams propose two different size options. Both options must stay within the 40-foot diameter limit and the 50-foot height limit. Both options must meet the 150,000-gallon minimum. Teams calculate each option's volume in cubic feet, then convert to gallons. Output: two labeled draft designs with volume math shown in full.
Session 3 — Cost analysis: Teams write a cost equation for each supplier, using cubic feet of tank volume as the variable. Teams solve the system to find the break-even point, the volume where both suppliers cost the same. Teams then find the actual dollar cost of each of their two draft designs, under both suppliers. That is four total cost calculations. Output: a completed cost table, checked against the $210,000 budget.
Session 4 (final session) — Choose, refine, and present: Using the cost table, teams pick one final tank size and one supplier. The choice must fit the budget and meet the storage rule. Teams finish their spec sheet and proposal, then present both to the class. One team member role-plays a Water Board member asking a question. Output: a finished spec sheet, proposal, and short presentation.

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

Rubric

Criterion	Emerging	Developing	Proficient	Advanced
Volume and constraint compliance	Volume calculation is missing or does not use the cylinder formula correctly	Volume is calculated but the design does not clearly meet the 150,000-gallon minimum or the zoning limits	Final design's volume is correctly calculated and clearly meets the storage minimum and both zoning limits	Final design meets all constraints and the proposal explains the margin above the 150,000-gallon minimum
Cost analysis and budget	No system of equations is shown, or the final design's cost is not checked against the budget	System of equations is attempted but contains errors, or only one supplier's cost is checked	System of equations is solved correctly and both suppliers' costs are checked against the $210,000 budget for the final design	System of equations is solved correctly, both suppliers are checked, and the proposal explains why the chosen supplier is cheaper using the break-even cubic footage
Presentation and proposal	Proposal is incomplete or the spec sheet is missing key measurements	Proposal covers the design but does not clearly explain the reasoning behind the supplier choice	Proposal clearly explains how the design meets both the storage requirement and the budget	Proposal clearly explains both constraints and anticipates a likely question from the Water Board about cost or capacity

Differentiation

Support

Provide the warm-up calculation from Session 1 fully worked out as a model, and give teams one pre-approved diameter-and-height combination that meets all constraints for Session 2, so they can focus their time on the cost analysis in Session 3.

Extension

Ask teams to calculate what tank diameter (keeping the height at their chosen design's value) would exactly hit the 150,000-gallon minimum with no extra margin, and to explain in the written proposal why building to the exact minimum might not be a wise real-world choice.

ELL supports

Provide a labeled diagram of a cylindrical water tower showing diameter and height before Session 1, and allow the written proposal to include labeled sketches and a filled-in cost table alongside shorter sentences rather than full paragraphs.

Extensions

Have teams calculate (using only the cost figures given in this fictional project, not outside sources) what percent of the $210,000 budget their final chosen design actually uses, and present that percentage alongside their spec sheet as a measure of how much budget margin the Water Board would still have available.