Quiz & test questions Grade 10 Math
Silverton Standpipe Geometry and Hydraulics Quiz
A 30-point grade 10 quiz mixing multiple choice, computation, and short answer on cylinder volume, pressure from height, and continuity for a fictional water district.
Objectives
- Students will compute the volume of a cylindrical standpipe in cubic feet and gallons.
- Students will apply pressure-from-height and the continuity equation to a distribution system.
Vocabulary
- Standpipe
- A standpipe is a tall, cylindrical water storage tank that sits directly on the ground instead of standing on legs like a water tower. It stores water and helps maintain steady pressure in the pipes nearby.
Also: cylinder volume, pressure, continuity
Teacher overview
This 30-point quiz checks whether grade 10 students can apply geometry and hydraulics to a distribution system at the fictional Silverton Water District. It mixes two multiple-choice items, four computation items, and two short-answer items across cylinder volume, pressure from water height, and the continuity equation. Each item states its point value.
Assessment
The Silverton Water District (a fictional district) stores water in a cylindrical standpipe 30 feet in diameter with 40 feet of water depth. Use these facts where needed: cylinder volume (cu ft) = 0.785 × diameter² × depth; 1 cubic foot = 7.48 gallons; pressure (psi) = height (ft) × 0.433; and flow Q = area × velocity. Most states require at least 20 psi at every connection, and utilities aim for 40 to 80 psi.
(3 points) Which expression gives the standpipe's volume in cubic feet?
- A) 0.785 × diameter × depth
- B) 0.785 × diameter² × depth
- C) 2.31 × diameter² × depth
- D) diameter² × depth
(4 points) Using volume = 0.785 × diameter² × depth, find the standpipe's volume in cubic feet.
(4 points) Convert the volume from item 2 to gallons using 1 cubic foot = 7.48 gallons.
(3 points) The water surface stands 120 feet above a home. Using pressure = height × 0.433, the pressure at the home is closest to:
- A) 28 psi
- B) 52 psi
- C) 92 psi
- D) 277 psi
(4 points) A distribution pipe has a cross-sectional area of 0.8 square feet and carries water at 3.5 feet per second. Using Q = area × velocity, find the flow in cubic feet per second.
(4 points) Convert the flow from item 5 to gallons per minute using 1 cfs = 448.8 gpm.
(3 points) The home's pressure from item 4 is about 52 psi. Utilities aim for 40 to 80 psi. Is 52 psi within that target range? Answer yes or no and explain in one sentence.
(5 points) A second home sits 200 feet below the standpipe's water surface. Find its water pressure, then explain in one sentence why the district might install a pressure-reducing valve there.
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: B) 0.785 × diameter² × depth. This is the standard formula for the volume of a cylinder written with diameter, so it is the correct choice.
Answer: 28,260 cu ft. Volume = 0.785 × 30² × 40 = 0.785 × 900 × 40 = 28,260 cubic feet.
Answer: 211,385 gal. 28,260 cubic feet × 7.48 gallons per cubic foot = 211,384.8, about 211,385 gallons.
Answer: B) 52 psi. Pressure = 120 × 0.433 = 51.96, which rounds to 52 psi, the closest choice.
Answer: 2.8 cfs. Q = area × velocity = 0.8 square feet × 3.5 feet per second = 2.8 cubic feet per second.
Answer: 1,257 gpm. 2.8 cfs × 448.8 gpm per cfs = 1,256.64, about 1,257 gpm.
Answer: Yes. 52 psi falls between 40 and 80 psi, so the home's pressure is inside the target range utilities aim for.
Answer: 86.6 psi. Pressure = 200 × 0.433 = 86.6 psi. Because that is above the 80 psi comfort ceiling, the district might install a pressure-reducing valve to protect the home's plumbing and fixtures.
Differentiation
Support
Provide a formula card listing the four relationships used on the quiz, and mark item 2 with the values already placed (0.785 × 30² × 40) so students can focus on the arithmetic. Allow a calculator on every item.
Extension
Ask students to find the water height, in feet, that would produce exactly 65 psi at a home in the fictional district, working backward through pressure = height × 0.433. Then have them state whether that height is above or below the standpipe's 40-foot water depth and what that implies for hilltop service.
ELL supports
Provide a labeled diagram of the standpipe showing diameter, water depth, and the height of water above two homes at different elevations. Allow short-answer items 7 and 8 to be completed with the numeric work plus a brief phrase rather than a full sentence.