Worksheet Grade 11 Math

Tilbourne Hollow's Detention Basin: Volume, Storage, and Drawdown

A grade 11 worksheet on a fictional town's stormwater detention basin, using sloped-side geometry, acre-feet, design-storm runoff, and drawdown time.

Grade: Grade 11
Subject: Math
Material: Worksheet
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: Items 1 through 3 model the sloped-side basin as a rectangular frustum, using the floor rectangle, the side-slope ratio, and the average-end-area rule to describe an earthwork structure by its measures.

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: Items 4, 5, 8, 9, 11, and 12 carry the same water through cubic feet, gallons, acre-feet, cubic feet per second, gallons per minute, and hours, so the units guide each step of the multi-step solution.

All materials for HSN-Q.A.1 →

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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 compute the volume of a basin with sloped sides using the average-end-area method.
Students will convert a storage volume among cubic feet, gallons, and acre-feet.
Students will find a design-storm runoff volume from a composite runoff coefficient and compare it against available storage.

Vocabulary

Detention basin: A detention basin is a dug-out area that fills with stormwater during a storm and then slowly drains empty over hours or days. It holds the water back so streets and streams downstream do not flood.
Acre-foot: The amount of water it takes to cover one acre of land, about the size of a football field, one foot deep. Western states use acre-feet to measure large amounts of water.

Also: side slope, freeboard, runoff coefficient

Teacher overview

A stormwater detention basin holds the runoff from a storm and lets it out slowly through a small outlet, so the shape of the basin sets how much it can hold while the outlet sets how long it takes to empty. This worksheet follows a basin proposed for a new subdivision in the fictional town of Tilbourne Hollow, where the sides slope outward and the floor is a plain rectangle. Students who treat the basin as a box and use the top dimensions throughout will overstate the storage by more than a third, and items 1 through 3 are arranged to expose that error before the later items depend on it.

Tilbourne Hollow's Detention Basin: Volume, Storage, and Drawdown — Grade 11 Math

Name: ____________________________ Date: ______________

Student Worksheet

The town of Tilbourne Hollow is fictional, and so are the basin and the subdivision described here. Use these values for every item.

The basin floor is a rectangle 120 ft long and 60 ft wide.
Every side slopes outward 3 ft for each 1 ft of rise.
The basin is 6 ft deep, measured from the floor to the top of the embankment.
Average-end-area rule: volume = (floor area + top area) divided by 2, times the depth.
The subdivision drains 12 acres in all: 3.2 acres of rooftop with a runoff coefficient of 0.9, 2.4 acres of street and driveway with a coefficient of 0.9, and 6.4 acres of lawn with a coefficient of 0.2.
The design storm drops 2.5 inches of rain.
For these items, treat the basin as storing all of the storm's runoff first; the outlet then releases a steady 0.35 cfs.
Town policy calls for 1 ft of freeboard, so runoff may fill only the bottom 5 ft.
Conversions: 1 cubic foot = 7.48 gallons; 1 acre-foot = 43,560 cubic feet; 1 acre = 43,560 square feet; 1 cfs = 448.8 gallons per minute.

Where an item does not name a precision, round areas and volumes to the nearest whole unit and rates and times to the nearest tenth.

Find the area of the basin floor in square feet.
Find the area of the water surface at the top of the basin, 6 ft above the floor, in square feet.
Use the average-end-area rule to find the basin volume in cubic feet.
Convert the basin volume to gallons.
Convert the basin volume to acre-feet. Round to two decimal places.
Find the composite runoff coefficient for the 12 acres, weighting each coefficient by its area. Round to two decimal places.
Multiply the composite coefficient by the 2.5-inch design storm to find the depth of runoff in inches. Round to two decimal places.
Find the runoff volume in cubic feet for the whole 12 acres.
Convert the runoff volume to gallons.
What percent of the basin volume does the design-storm runoff fill? Round to one decimal place.
Convert the outlet release of 0.35 cfs to gallons per minute.
At that release rate, how many hours does the basin take to drain the design-storm runoff?
Find the storage available in the bottom 5 ft of the basin, in cubic feet, using the average-end-area rule again.
Compare your answers to items 8 and 13. Does the design storm fit under the freeboard rule? Explain what the town would have to change if it does not.

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: 7,200 sq ft.
The floor is a rectangle, so 120 ft x 60 ft = 7,200 square feet.
Answer: 14,976 sq ft.
Rising 6 ft adds 3 x 6 = 18 ft of width at each side, so the length grows by 36 ft and the width grows by 36 ft. The top measures 156 ft by 96 ft, and 156 x 96 = 14,976 square feet.
Answer: 66,528 cu ft.
The average of the two areas is (7,200 + 14,976) divided by 2 = 11,088 square feet. Multiplying by the 6 ft depth gives 11,088 x 6 = 66,528 cubic feet.
Answer: 497,629 gal.
66,528 cubic feet x 7.48 gallons per cubic foot = 497,629.4 gallons.
Answer: 1.53 acre-ft.
66,528 cubic feet divided by 43,560 cubic feet per acre-foot = 1.527 acre-feet, which rounds to 1.53.
Answer: 0.53.
Weight each coefficient by its area: (3.2 x 0.9) + (2.4 x 0.9) + (6.4 x 0.2) = 2.88 + 2.16 + 1.28 = 6.32. Dividing by the 12 acres gives 6.32 divided by 12 = 0.5267, which rounds to 0.53.
Answer: 1.32 in.
0.5267 x 2.5 inches = 1.3167 inches of runoff, which rounds to 1.32 inches.
Answer: 57,354 cu ft.
The drainage area is 12 x 43,560 = 522,720 square feet. The runoff depth in feet is 1.3167 divided by 12 = 0.10972 ft. Multiplying gives 522,720 x 0.10972 = 57,354 cubic feet.
Answer: 429,008 gal.
57,354 cubic feet x 7.48 gallons per cubic foot = 429,007.9 gallons.
Answer: 86.2 percent.
57,354 divided by 66,528 = 0.8621, or 86.2 percent of the basin volume.
Answer: 157.1 gpm.
0.35 cfs x 448.8 gallons per minute per cfs = 157.08 gallons per minute.
Answer: 45.5 hr.
At 0.35 cubic feet per second the outlet passes 0.35 x 3,600 = 1,260 cubic feet per hour. Then 57,354 divided by 1,260 = 45.52 hours.
Answer: 51,750 cu ft.
At a water depth of 5 ft the surface measures (120 + 30) by (60 + 30), or 150 ft by 90 ft, which is 13,500 square feet. The average of 7,200 and 13,500 is 10,350 square feet, and 10,350 x 5 = 51,750 cubic feet.
Answer: No, the design storm does not fit.
The runoff of 57,354 cubic feet is larger than the 51,750 cubic feet available below the freeboard line, so water would rise into the last foot of the embankment. Acceptable fixes include deepening the basin, widening the floor, flattening the side slopes, or routing part of the rooftop area to a separate infiltration area so less runoff reaches the basin. A larger outlet is not an acceptable fix, because the outlet is sized to limit how fast water leaves the site, and a bigger one would send more water downstream than the basin is built to allow.

Differentiation

Support

Give students a labeled cross-section drawing showing the 120 ft floor, the 6 ft depth, and the 3-to-1 side slope, with the added 18 ft marked at each side. Work items 1 through 3 together so the class agrees on the top dimensions before anyone works alone, and hand out a conversion card with the four conversions listed in the scenario.

Extension

Ask students to find the deepest water the basin can hold if the town keeps the same floor and side slopes but raises the embankment to 8 ft, then decide how much extra rooftop area the enlarged basin could serve at the same design storm. Students who finish early can graph stored volume against water depth and describe why that graph curves upward rather than rising in a straight line.

ELL supports

Pre-teach "floor," "embankment," "freeboard," "side slope," and "drawdown" with a sketch labeled in both English and the student's first language. Provide a three-column recording table with the headings "quantity," "formula," and "result" so students can show their work without composing full sentences, and allow the item 14 answer to be given as a labeled drawing with a one-sentence caption.

Extensions

Have students look up a stormwater design manual published by their own county or state, find the design storm depth that manual requires for a residential subdivision, and recompute items 7 through 10 with that rainfall depth in place of the 2.5 inches used here. A short written comparison of the two results makes a good bridge into a discussion of why design standards differ from one region to another.