Worksheet Grade 10 Math

Cragmont Wellfield: Drawdown and Casing Volume Worksheet

A grade 10 geometry worksheet where students find well drawdown, specific capacity, and casing water volume for a fictional town's groundwater production well.

Grade: Grade 10
Subject: Math
Material: Worksheet
Time: 40 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 4 through 7 model the standing water column inside the well casing as a cylinder and use its diameter and height to find capacity, the real-object modeling this standard describes.

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 1 through 9 carry units through a multi-step chain from feet of drawdown to cubic feet, gallons, and gallons per day when sizing the well's daily production.

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 calculate well drawdown and specific capacity from static and pumping water levels.
Students will model a well's standing water column as a cylinder and find its volume in cubic feet and gallons.
Students will scale a single well's daily output to a town's total demand.

Vocabulary

Drawdown: Drawdown is how far the water level in a well drops when a pump pulls water out. The harder and longer you pump, the bigger the drawdown gets.
Aquifer: An aquifer is an underground layer of rock, sand, or gravel that holds water in the tiny spaces between its grains. Wells reach down into aquifers to bring water up to the surface.

Also: static water level, specific capacity, casing

Teacher overview

The town of Cragmont, a fictional community invented for this worksheet, draws its drinking water from a wellfield tapping a sand-and-gravel aquifer. This worksheet follows one production well through a single pumping test. Students find the well's drawdown and specific capacity, model the water standing in the casing as a cylinder to find its volume, and scale one well's daily output up to the town's total demand. Working in one consistent set of units from feet to cubic feet to gallons is the discipline the problems are built to reinforce.

Cragmont Wellfield: Drawdown and Casing Volume Worksheet — Grade 10 Math

Name: ____________________________ Date: ______________

Student Worksheet

The town of Cragmont operates a groundwater production well. During a pumping test the crew recorded these measurements for the well.

Static water level (before pumping): 74 feet below the ground surface.
Pumping water level (while pumping at 300 gallons per minute): 110 feet below the ground surface.
Total drilled depth of the well: 250 feet.
Inside diameter of the well casing: 1.0 foot.

Use these facts for all problems:

Drawdown = pumping water level − static water level.
Specific capacity = pumping rate ÷ drawdown.
Cylinder volume (cubic feet) = 0.785 × diameter² × height.
1 cubic foot holds 7.48 gallons.

Find the well's drawdown, in feet, during the pumping test.
Find the well's specific capacity, in gallons per minute per foot of drawdown. Round to the nearest hundredth.
Before pumping starts, water stands from the static level (74 feet down) to the bottom of the well (250 feet down). Find the height of that standing water column, in feet.
Model the standing water column from item 3 as a cylinder 1.0 foot in diameter. Find its volume in cubic feet. Round to the nearest hundredth.
Convert the volume from item 4 to gallons. Round to the nearest tenth.
While the pump runs, the water level drops to 110 feet below the surface. Find the volume of the standing water column in gallons during pumping, again modeling it as a 1.0-foot cylinder. Round to the nearest tenth.
How many gallons of water leave the casing as the level falls from static (item 5) to pumping (item 6)?
The pump runs for 18 hours in one day at 300 gallons per minute. How many gallons does the well deliver that day?
The town of Cragmont needs 1.2 million gallons of water each day from the wellfield. Using the single-well daily output from item 8, how many wells like this one are needed to meet that demand?
Explain why your answer to item 9 must be rounded up to a whole number of wells rather than left as a decimal.
A second well is drilled into the same aquifer and pumped at the same time as the first. Explain what this is likely to do to the first well's drawdown, and therefore to its specific capacity.

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: 36 ft.
Drawdown = pumping water level − static water level = 110 − 74 = 36 feet.
Answer: 8.33 gpm per foot.
Specific capacity = pumping rate ÷ drawdown = 300 ÷ 36 = 8.333, which rounds to 8.33 gallons per minute per foot of drawdown.
Answer: 176 ft.
The water column runs from the static level to the bottom of the well: 250 − 74 = 176 feet.
Answer: 138.16 cu ft.
Volume = 0.785 × diameter² × height = 0.785 × 1.0² × 176 = 0.785 × 176 = 138.16 cubic feet.
Answer: 1,033.4 gal.
138.16 cubic feet × 7.48 gallons per cubic foot = 1,033.44, which rounds to about 1,033.4 gallons.
Answer: 822.1 gal.
During pumping the column runs from 110 feet down to 250 feet down, a height of 140 feet. Volume = 0.785 × 1.0² × 140 = 109.9 cubic feet. 109.9 × 7.48 = 822.05, which rounds to about 822.1 gallons.
Answer: 211.3 gal.
Water leaving the casing = static volume − pumping volume = 1,033.4 − 822.1 = 211.3 gallons.
Answer: 324,000 gal.
300 gallons per minute × 60 minutes per hour × 18 hours = 324,000 gallons in one day.
Answer: 4 wells.
1,200,000 gallons per day ÷ 324,000 gallons per well per day = 3.70 wells, which must be rounded up to 4 wells.
Answer: A partial well cannot supply water.
A well is either drilled or not, so 3.70 wells has no physical meaning. Three wells would deliver only 972,000 gallons per day, short of the 1,200,000 gallons needed, so the town must build a fourth well to cover the remaining demand.
Answer: Drawdown increases and specific capacity falls.
Two wells pumping the same aquifer lower the water table around each other, an effect called interference. The first well's pumping level drops further, so its drawdown grows. Because specific capacity is pumping rate ÷ drawdown, a larger drawdown at the same rate means a lower specific capacity.

Differentiation

Support

Provide the drawdown (36 feet) already calculated before item 2, and give students a printed reference strip listing the cylinder-volume formula and the 7.48 gallons-per-cubic-foot conversion so they do not need to recall them. Work item 3 through together as a class before students attempt items 4 through 7.

Extension

Ask students to find the pumping rate that would double the well's specific capacity if the drawdown stayed at 36 feet, then explain why a real aquifer usually will not allow that rate without a much larger drawdown.

ELL supports

Provide a labeled cross-section diagram of the well showing the ground surface, static water level, pumping water level, and the bottom of the casing, with each level marked in feet. Allow students to show their work on the diagram with numbers and short phrases rather than full sentences for items 1 through 9.