Lesson 11Stained-Glass Windows

Let’s use circumference and area to design stained glass windows.

Learning Targets:

I can apply my understanding of area and circumference of circles to solve more complicated problems.

11.1 Cost of a Stained-Glass Window

The students in art class are designing a stained-glass window to hang in the school entryway. The window will be 3 feet tall and 4 feet wide. Here is their design.

A stained glass window composed of six rectangular panels of equal size. The six panels are arranged two across and three down to form a three foot by four foot rectangle. Four panels are composed of two half circles and four quarter circles of clear glass that are tangent to each other. The two radii of the quarter circles are on both the horizontal and vertical sides of the rectangule and the diameter of the semi circles are on the horizontal side of the rectangle. The remaining regions in the panel are composed of colored glass. Two panels are composed of four half circles of clear glass that are tangent to each other. The diameters of the semi circles are on the horizontal sides of the rectangular panel and are half the length of the horizontal side. The remaining regions in the panel are composed of colored glass.

They have raised $100 for the project. The colored glass costs $5 per square foot and the clear glass costs $2 per square foot. The material they need to join the pieces of glass together costs 10 cents per foot and the frame around the window costs $4 per foot.

Do they have enough money to cover the cost of making the window?

11.2 A Bigger Window

A local community member sees the school’s stained glass window and really likes the design. They ask the students to create a larger copy of the window using a scale factor of 3. Would $450 be enough to buy the materials for the larger window? Explain or show your reasoning.

11.3 Invent Your Own Design

Draw a stained glass window design that could be made for less than $450. Show your thinking. Organize your work so it can be followed by others.