Bell Work:Indicate if the following numbers are elements of the set of integers. Use the proper symbolsa) -1b) 2c) √3

Answer:a) Yesb) Yesc) No

Lesson 91: Effect of Scaling on Perimeter, Area, and Volume

In many lessons and problems, we have noted the effect of changing dimensions on the perimeter, area, surface area, and volume of various figures. These effects are summarized in the next table. If the dimensions (length, width, height) of a figure or object are changed proportionally (by a scale factor), then these ratios between the two figures apply.

Scale FactorRatio of perimeters = scale factor

Ratio of areas = (scale factor)Ratio of volumes = (scale factor)

2

3

In this lesson we will review these relationships with a variety of examples.

Example:Vince was asked to paint a mural near the city park based on a painting he made in art class. The mural was to be ten times the length and width of his original canvas painting. Vince bought ten times as much paint as he used for his original painting, yet he ran out of paint after only a fraction of the mural was painted. Why did Vince run out of paint so quickly? How much paint did he need? Explain.

Answer:The dimensions of his painting are increased by a factor of 10, so the area of the mural is 100 times the area of the canvas. He needs to buy 100 times as much paint as he used for his original painting.

Example:Irene works with stained glass. She wants to make a replica of a stained glass window. Her replica will be related to the original window by a scale factor of 1/3. the original window is made of 3456 square inches of glass and has a perimeter of 240 inches. How much glass will Irene use in the replica? What will be the perimeter of her replica?

Answer:1/9(3456 in. ) = 384 in.1/3(240 in.) = 80 in.

2 2

Example:Nelson built this figure with four one-inch cubes. How many one-inch cubes are needed to build a similar figure with the dimensions doubled?

Answer:Scale factor is 2. Volume scale factor is 8.8 times as many cubes are needed to build the new figure.32 cubes are needed.

HW: Lesson 91 #1-25