Worksheet Grade 9 Art & Music

Scaling a Norwick Water Tower Mural: A Grade 9 Geometry Worksheet

Grade 9 art and geometry worksheet where students model a water tower tank as a cylinder and scale a mural design using linear and area scale factors.

Grade: Grade 9
Subject: Art & Music
Material: Worksheet
Time: 40 min
Prep: No prep
Materials: None

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: Students model the tower's tank as a cylinder and use its circumference and lateral surface area to find the real curved area a wrap-around mural must cover.

All materials for HSG-MG.A.1 →

HSN-Q.A.2 Common Core Math

Define appropriate quantities for the purpose of descriptive modeling.

How this material aligns: Item 10 asks students to decide whether square feet or gallons of paint is the appropriate quantity to give the crew, choosing the measure that answers the ordering question.

All materials for HSN-Q.A.2 →

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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 circumference and lateral surface area of a cylindrical tank.
Students will apply a linear scale factor and its squared area factor to a mural design.
Students will choose the quantity that best answers a real purchasing question.

Vocabulary

Key words: circumference, lateral surface area, cylinder, scale factor, proportion

Teacher overview

Norwick is a fictional town whose new elevated water tank will carry a community mural on its outside curved surface. The tank is a cylinder with a diameter of 40 feet and a height of 30 feet. Students are planning the mural on paper at a scale of 1 inch to 10 feet, and the paint they will use covers 300 square feet per gallon. This worksheet asks students to model the round tank with cylinder geometry, then scale their design up correctly, including the way area grows faster than length when a drawing is enlarged. Use 3.14 for pi and round each answer as the item asks.

Scaling a Norwick Water Tower Mural: A Grade 9 Geometry Worksheet — Grade 9 Art & Music

Name: ____________________________ Date: ______________

Student Worksheet

Use these shared facts for every item: the tank is a cylinder 40 feet across and 30 feet tall, the design scale is 1 inch to 10 feet, and the paint covers 300 square feet per gallon.

Find the distance around the tank (its circumference) using circumference = pi times diameter. Round to the nearest foot.
The mural covers the whole curved side of the tank. Find that lateral surface area using the unrounded circumference from item 1 (125.6 feet) times height. Round to the nearest square foot.
The design sketch is a long rectangle that represents the full wrap-around. At 1 inch to 10 feet, how many inches wide should the sketch be to match the circumference? Round to the nearest tenth of an inch.
At the same scale, how many inches tall should the sketch be to match the 30-foot tank height?
On the sketch, a leaping fish is drawn 4 inches long. How long will that fish be on the finished mural, in feet?
When the scale is 1 inch to 10 feet, one square inch on the sketch stands for how many square feet on the tank?
A painted wave area measures 6 square inches on the sketch. How many square feet will it cover on the tank?
Using your lateral surface area from item 2 and the coverage of 300 square feet per gallon, how many whole gallons of paint must the crew buy to cover the curved surface once?
Explain why the design must be planned as a long rectangle rather than a square, even though the tank is round.
The town can describe the job to the paint crew either as a number of square feet or as a number of gallons. Which quantity should the crew be given to place their paint order, and why?

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: 126 ft. Circumference = 3.14 x 40 = 125.6 feet, which rounds to 126 feet.
Answer: 3,768 sq ft. Lateral surface area = circumference x height = 125.6 x 30 = 3,768 square feet.
Answer: 12.6 in. The full circumference is 125.6 feet, and 125.6 divided by 10 feet per inch = 12.56 inches, which rounds to 12.6 inches.
Answer: 3 in. The tank is 30 feet tall, and 30 divided by 10 feet per inch = 3 inches.
Answer: 40 ft. At 1 inch to 10 feet, 4 inches x 10 feet per inch = 40 feet.
Answer: 100 sq ft. Area scales by the square of the linear factor: 10 x 10 = 100 square feet for each square inch.
Answer: 600 sq ft. Each square inch stands for 100 square feet, so 6 x 100 = 600 square feet.
Answer: 13 gallons. 3,768 square feet divided by 300 square feet per gallon = 12.56, and the crew must round up to 13 whole gallons to cover the surface.
Answer: The mural wraps the curved side, and unrolling a cylinder's side gives a rectangle whose width equals the circumference and whose height equals the tank height, so a long rectangle fits the surface while a square would not.
Answer: Gallons of paint. The crew buys paint by the gallon, so gallons answers the purchasing question directly, while square feet is the area they must first convert into gallons using the coverage rate.

Differentiation

Support

Provide the circumference and lateral surface area from items 1 and 2 already worked, so students can focus on the scaling items 3 through 8. Give a labeled sketch of an unrolled cylinder so the rectangle idea in item 9 is visible before they explain it.

Extension

Ask students to redesign the mural so it uses two coats of paint, recompute the gallons needed, and then propose a design change that would keep the painted area under a set number of gallons while still covering the visible front of the tank.

ELL supports

Provide a labeled diagram showing diameter, circumference, and height on the cylinder, with a home-language gloss where possible. Offer sentence frames for items 9 and 10, such as "The design is a rectangle because the curved side unrolls into ___." Allow students to answer with labeled sketches alongside short phrases.

Extensions

Students can measure a real cylindrical object in the room, such as a trash can or a column, model it as a cylinder, and design a scaled wrap-around label for it using the same circumference and area-scale reasoning they practiced on the tower.