Dimensions Changes



Dimension ChangesACTIVITY ONEAs the dimensions of a polygon change, how does the perimeter change? How does the area change? You will explore these questions using the figures below. Figure #1 Figure #2 Figure #3Fill in the chart below with information from the first three figures.Figure #LengthWidthPerimeterArea1234Describe how the length and width are changing with each figure.Write ratios to compare each new perimeter to the previous figure. For example, compare figure 2 and 1, 3 and 2, etc. Describe the changes in the perimeter. How many times larger is the perimeter for each new figure?Write ratios to compare each new area to the previous figure as in problem #1. Describe the changes in the area. How many times larger is the area for each new figure?Draw the next figure in the pattern. Can you predict what the perimeter and area will be? Explain how you made your prediction.Fill in the information in the chart for figure #4. Was your prediction correct?Write a general rule to describe how the (a) perimeter and (b) area of a polygon changes if the dimensions are doubled.What is the perimeter of the rectangle below? _________ The area? _______4 cm3 cmIf the dimensions are increased by a scale factor of 3, what is the new perimeter?_____________ The new area? __________Write a ratio comparing the new perimeter to the original perimeter. _______How many times larger is the new perimeter? __________What general statement can be made that describes the change in perimeter when the dimensions are changed by a scale factor of 3?Write a ratio comparing the new area to the original area. _____________How many times larger is the new area? ______________Write a rule that describes the change in area when the dimensions of a polygon are enlarged by a scale factor of 3.5 cm10 cm8 cm5 cm8 cm4 cm3 cm4 cm16 cm12 cmDo both the rules you have written work for other polygons? Try them with the triangle, parallelogram, and trapezoid below. Scale Factor: 2Scale Factor:3 Scale Factor: ?Perimeter:Perimeter: Perimeter:Area:Area: Area: Write a general rule to describe how the perimeter and area of a figure change if the dimensions are changed by any scale factor. Use the rules you have written to answer the following questions.A rectangle has an area of 24 cm2. The dimensions of the rectangle are changed proportionally and the new rectangle has an area of 96 cm2. Find the dimensions of the new rectangle (there are more than one).Ellen has a poster with an area of 576 square inches. Susan is making a replica of the poster that will be 64 square inches. What scale factor will Susan use to change the dimensions of her poster? Diane is creating a pattern for a rectangular rug that will go in her living room. Her original pattern will be increased so that the dimensions of the actual rug are 4 times larger. By how much will the area increase?ACTIVITY TWOIf you take a unit cube and increase all three dimensions by the scale factor in the table below. For example, to make a new cube that has a scale factor of 2:1, you would double the length, width, and height. The new cube would have dimensions of 2 by 2 by 2 and a volume of 8 cubic units. Fill in the chart with the dimensions and volume of the new cubes. Scale FactorDimensions in cmVolume in cm3Exponent Form1:11 X 1 X 11132:12 X 2 X 2 8233:14:15:110:1nWrite each volume in exponent form. For example, a volume of 1 is 13 and 8 is 23 . Describe any patterns that you see as the dimensions are changed. 2 cm5 cm4 cmA prism has the following dimensions. Find the volume _______________ Increase the dimensions by a scale factor of 2. Draw the figure below. Be sure to label the dimensions.What is the new volume? ________Write a ratio to compare the new volume with the original volume. How much larger is the new volume than the original volume? ______________________________________Does this relate to the pattern in your chart? In what way?A rectangular prism with the following dimensions: Length 6 cmFind the volume. _________ Width 3 cm Height 2 cmIncrease the dimensions by a scale factor of 2. Draw and label the new figure and find the volume. __________Write a ratio to compare the new volume to the original volume. How much larger is the new volume than the original volume? Write a general rule to find the volume of a rectangular prism if the dimensions are increased by a scale factor of 2.Use the dimensions in problem #3 to describe a prism with dimensions that are increased by a scale factor of 3. Draw and label the prism.Find the volume of the new prism. ____________________________Write a ratio to compare the new volume to the original volume. How much larger is the new volume than the original volume?Write a rule that describes the change in volume when the dimensions of a polygon are enlarged by a scale factor of 3.What if the dimensions for the rectangular prism below are cut in half. Predict the scale factor of the new volume. _____________Original volume _______________ 10 cm 6 cm12 cmDraw and label the new prism and find the volume. Was your prediction correct? Write a rule that describes the change in volume when the dimensions of a polygon are decreased by a scale factor of ? .Write a rule that describes the change in volume for any scale factor.2.Try these. Use your rules to find the volume if the figure is changed by a scale factor of 2; ?; 3.1. 4 cm8 cm6 cmVolume: 84 cm3VOLUMEProblem 1Problem 2SF:2SF: ?SF:3The volume for the prism below is 840 cm3. The smaller prism has dimensions that are half the size of the larger carton. What is the volume of the smaller prism.?Volume = 840 cm3 Volume = ? Two rectangular prisms are drawn below. If the ratio of the volumes of the large prism to the small prism is 64:1, what are the dimensions of the large cube? 3cm6cm5cm ................
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