Worksheet Grade 10 Math
Wolvercote Park-and-Ride Lot: Sizing an Infiltration Trench
A grade 10 worksheet where students size a gravel infiltration trench for a fictional parking lot using runoff volume, void space, and a 72-hour drawdown limit.
Objectives
- Students will calculate runoff volume from a paved area and a design storm depth.
- Students will size a gravel trench so its void space stores the full runoff volume.
- Students will test a trench design against a length limit and a drawdown time limit.
Vocabulary
- Infiltration
- Infiltration is when rain or melted snow soaks down into the soil instead of flowing away across the top of it. Water that infiltrates can feed plant roots or keep sinking to become groundwater.
Also: design storm, runoff, void space, drawdown time
Teacher overview
Wolvercote is a fictional town, and the lot dimensions, soil rate, and design storm below are set for this worksheet. Students find how much runoff a repaved commuter lot produces, then size a gravel-filled trench to hold that water while it soaks into the ground. The misconception this worksheet targets is sizing the trench to equal the runoff volume; gravel is mostly stone, so only the void space between stones holds water, and a trench must be roughly three times the runoff volume when the void space is 35 percent. Students also tend to leave the soil rate in inches per hour when the stored volume is in cubic feet, which makes drawdown times far too small.
Student Worksheet
The town of Wolvercote is fictional, and every measurement here is set for this worksheet. Use these facts where needed: paved area (square feet) × rainfall (inches) × 0.623 = gallons of runoff; 1 cubic foot holds 7.48 gallons; 1 foot = 12 inches.
The town is repaving a park-and-ride lot that measures 180 feet by 260 feet, all of it asphalt. The design storm is 1.2 inches of rain. Engineers plan a gravel infiltration trench along one edge of the lot. The gravel has 35 percent void space, the soil beneath the trench takes water in at 0.5 inches per hour, and town rules require the stored water to drain within 72 hours.
Find the paved area of the lot in square feet.
Find the runoff from the 1.2-inch design storm in gallons. Round to the nearest gallon.
Convert your item 2 answer to cubic feet. Round to the nearest cubic foot.
Only 35 percent of the trench holds water, because the rest is stone. Find the total trench volume, in cubic feet, needed to store the item 3 runoff.
The first design is 10 feet wide and 5 feet deep. Find the trench length needed, rounded up to the next whole foot.
The longest straight run available along the lot edge is 260 feet. Does the item 5 trench fit? Answer yes or no.
The engineers keep the 10-foot width and deepen the trench to 6 feet. Find the new length, rounded up to the next whole foot.
Find the bottom area of the item 7 trench in square feet.
Water leaves through the trench bottom at 0.5 inches per hour. Convert that rate to cubic feet per hour for the item 8 bottom area. Round to the nearest tenth.
Using the item 3 runoff volume and the item 9 rate, find the drawdown time in hours. Round to the nearest tenth.
Town rules require drainage within 72 hours. Does the item 7 design meet that rule? Answer yes or no.
Explain in two or three sentences why the trench volume in item 4 must be larger than the runoff volume in item 3.
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: 46,800 square feet. 180 feet × 260 feet = 46,800 square feet of asphalt.
Answer: 34,988 gallons. 46,800 × 1.2 × 0.623 = 34,987.68 gallons, which rounds to 34,988 gallons.
Answer: 4,678 cubic feet. 34,988 ÷ 7.48 = 4,677.5 cubic feet, which rounds to 4,678 cubic feet.
Answer: 13,366 cubic feet. 4,678 ÷ 0.35 = 13,365.7, which rounds to 13,366 cubic feet of trench.
Answer: 268 feet. The cross-section is 10 × 5 = 50 square feet, so 13,366 ÷ 50 = 267.3 feet, rounded up to 268 feet.
Answer: No. The trench needs 268 feet, and only 260 feet of straight run is available, so the design does not fit.
Answer: 223 feet. The cross-section is now 10 × 6 = 60 square feet, so 13,366 ÷ 60 = 222.8 feet, rounded up to 223 feet, which fits inside 260 feet.
Answer: 2,230 square feet. The bottom is 10 feet × 223 feet = 2,230 square feet.
Answer: 92.9 cubic feet per hour. First convert the rate: 0.5 ÷ 12 = 0.04167 feet per hour. Then 2,230 × 0.04167 = 92.92, which rounds to 92.9 cubic feet per hour.
Answer: 50.4 hours. 4,678 ÷ 92.9 = 50.35 hours, which rounds to 50.4 hours.
Answer: Yes. The trench drains in 50.4 hours, which is less than the 72-hour limit.
Answer: The trench is filled with stone, and water can sit only in the gaps between the stones. With 35 percent void space, roughly two-thirds of the trench is solid rock. The excavated volume must therefore be about three times the runoff volume for the gaps alone to hold the storm.
Differentiation
Support
Provide a sketch of a jar of gravel with the water line drawn in, labeled to show that only the gaps hold water, before students attempt item 4. Give the runoff formula with the item 2 numbers already substituted, and supply the 0.5 inches per hour rate already converted to 0.04167 feet per hour for item 9.
Extension
Ask students to find the trench width that would let a 5-foot-deep trench fit within the 260-foot run, then state whether that width is practical for a strip beside a parking lot. A second challenge is to find the design storm depth, in inches, that the 223-foot trench could handle if it were filled to capacity.
ELL supports
Provide a labeled cross-section drawing of the trench showing width, depth, length, and the gravel void space, with each term written beside the part of the drawing it names. Allow students to answer items 6 and 11 with the word yes or no plus a circled number rather than a full sentence.
Extensions
Have students measure a paved area at their own school, choose a design storm depth their teacher supplies, and repeat items 1 through 7 for a trench along its edge. Comparing the required trench length with the space actually available shows why designers in the fictional Wolvercote example had to change the depth rather than the width.