Lesson plan Grade 10 Art & Music
Wrapping the Selkirk Water Tower: A Grade 10 Surface-Area Design
A grade 10 art and design lesson where students size a painted graphic wrap for a cylindrical water tower using lateral surface area and a scale mock-up.
Objectives
- Students will model an elevated water tank as a cylinder and calculate its lateral surface area.
- Students will use a scale mock-up to plan how a graphic enlarges from paper to the full tank.
- Students will estimate the paint coverage a full-size graphic wrap requires.
Vocabulary
Key words: lateral surface area, scale factor, cylinder, mock-up
Teacher overview
Many towns paint graphics on their elevated water tanks, and designing such a graphic is a real commission a utility can approve. This lesson gives students the calculation a crew needs before painting begins: the lateral surface area of the cylindrical band that will carry the artwork, and a scale mock-up that shows how a small drawing maps onto that band. A common misconception is that enlarging a design by a linear scale factor also increases the paint needed by that same factor; students should leave understanding that paint tracks area, which is why the surface-area figure, not the drawing's height, sets the order.
Procedure
Hook (5 min): Project two or three photographs of painted municipal water towers and ask students what measurements a crew would need before ordering paint. Record answers on the board without correcting them; most classes name height but not the distance around, which sets up the circumference idea.
Model the method (12 min): On the board, model the calculation on a practice tank that is not on the student handout: a cylindrical band 30 feet in diameter and 20 feet tall. Show that the band is a rectangle when unrolled, so its area is the circumference times the height, or pi times diameter times height: 3.14 times 30 times 20 equals 1,884 square feet. Then model a scale mock-up in which 1 inch stands for 3 feet, converting the 20-foot height to a 6.7-inch drawing height.
Design and guided calculation (18 min): In teams of three, students sketch a simple graphic (one image and a short phrase) on grid paper, then complete handout questions 1 through 3 for the Selkirk tank, finding the band's area, the mock-up height, and the wrap length around the tank.
Independent calculation (10 min): Each student completes handout questions 4 and 5 individually, estimating the whole gallons of enamel the single-coat and two-coat jobs require.
Formative check and closure (5 min): As an exit ticket, students answer one item on an index card: a tank band has a circumference of 100 feet and a height of 20 feet; find its lateral area. Collect the cards and scan for the correct method (circumference times height, giving 2,000 square feet) before dismissal; reteach the next day if more than a quarter miss the method.
Student Handout
Selkirk (a fictional town) is repainting its elevated water tank. The cylindrical band that will carry the painted graphic is 36 feet across (its diameter) and 24 feet tall. Design your graphic on a scale mock-up where 1 inch represents 3 feet. Use 3.14 for pi, and assume one gallon of exterior enamel covers 350 square feet.
- The painted band is a cylinder 36 feet in diameter and 24 feet tall. Using lateral surface area equal to pi times diameter times height, find the band's area in square feet.
- On the mock-up, 1 inch represents 3 feet. How tall, in inches, is the 24-foot band on your mock-up?
- The band wraps all the way around the tank, a distance equal to the circumference (pi times diameter). Find that circumference in feet, then its length on the mock-up in inches.
- Assume one gallon of enamel covers 350 square feet. How many whole gallons must the crew buy to paint the band once? Round up to a whole gallon.
- The finished design calls for two coats. How many whole gallons are needed to paint the band twice? Round up to a whole gallon.
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: 2,713 square feet. Lateral area equals pi times diameter times height: 3.14 times 36 times 24 equals 2,712.96, which rounds to 2,713 square feet.
- Answer: 8 inches. At 1 inch per 3 feet, 24 feet divided by 3 equals 8 inches.
- Answer: 113 feet around, about 37.7 inches on the mock-up. Circumference equals 3.14 times 36 equals 113.04 feet; dividing by 3 gives 37.68 inches, about 37.7 inches on the mock-up.
- Answer: 8 gallons. 2,713 square feet divided by 350 square feet per gallon equals 7.75 gallons, which rounds up to 8 whole gallons.
- Answer: 16 gallons. Two coats cover 2 times 2,713, or 5,426 square feet; 5,426 divided by 350 equals 15.5, which rounds up to 16 whole gallons.
Differentiation
Support
Provide the unrolled-cylinder diagram (a rectangle labeled with circumference along the bottom and height up the side) so the lateral-area formula is visible rather than memorized. Give the circumference from question 3 already calculated before students attempt the paint estimate, so the arithmetic load falls on the division they are practicing.
Extension
Ask students to find the paint needed if the design were scaled so its linear dimensions doubled on a taller, wider replacement tank, and to explain in writing why the paint requirement roughly quadruples rather than doubles, connecting the result to area scaling by the square of the linear factor.
ELL supports
Pre-teach "diameter," "circumference," "lateral," and "coat" with a labeled diagram and a physical prop, such as a wrapped soup-can label peeled flat to show the rectangle. Provide a sentence frame for the extension writing: "When the design gets ___ times taller and wider, the paint needed becomes about ___ times as much because ___."