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04/26/11 Changing Dimensions LT: I will describe how increasing or decreasing a measurement will affect area and volume. Warm-Up Find the volume and surface area to the nearest tenth. V= 4,069.4 m3 SA=1582.6 m2 Today’s Plan: -Warm up -Changing Dimensions -Assignment LT: I will describe how increasing or decreasing a measurement will affect area and volume. 04/26/11 Changing Dimensions LT: I will describe how increasing or decreasing a measurement will affect area and volume. Predict: What affect will tripling the length, width, or height have on the volume of a rectangular prism? What if the length, width, AND height were tripled? Today’s Plan: -Warm up -Changing Dimensions -Assignment LT: I will describe how increasing or decreasing a measurement will affect area and volume. A box measures 5 in. by 3 in. by 7 in. Explain whether tripling the length, width, or height of the box would triple the volume of the box. 7 in 3 in 5 in The original box has a volume of (5)(3)(7) = 105 cm3. V = (15)(3)(7) = 315 cm3 Tripling the length would triple the volume. Try This: Example 2A A box measures 5 in. by 3 in. by 7 in. Explain whether tripling the length, width, or height of the box would triple the volume of the box. The original box has a volume of (5)(3)(7) = 105 cm3. V = (5)(3)(21) = 315 cm3 Tripling the height would triple the volume. Try This: Example 2A A box measures 5 in. by 3 in. by 7 in. Explain whether tripling the length, width, or height of the box would triple the volume of the box. The original box has a volume of (5)(3)(7) = 105 cm3. V = (5)(9)(7) = 315 cm3 Tripling the width would triple the volume. Try This: Example 2A A box measures 5 in. by 3 in. by 7 in. Explain what tripling the length, width, and height of the box will do. The original box has a volume of (5)(3)(7) = 105 cm3. V = (15)(9)(21) = 2835 cm3 Tripling the length, width, and height would make the volume 27 times bigger! 04/26/11 Changing Dimensions LT: I will describe how increasing or decreasing a measurement will affect area and volume. Predict: What affect will tripling the radius or height have on the volume of a cylinder? Today’s Plan: -Warm up -Changing Dimensions -Assignment LT: I will describe how increasing or decreasing a measurement will affect area and volume. Try This: Example 2B A cylinder measures 3 cm tall with a radius of 2 cm. Explain whether tripling the radius or height of the cylinder would triple the amount of volume. The original cylinder has a volume of 4 • 3 = 12 cm3. V = 4 • 9 = 36 cm3 Tripling the height would triple the volume. Try This: Example 2B A cylinder measures 3 cm tall with a radius of 2 cm. Explain whether tripling the radius or height of the cylinder would triple the amount of volume. The original cylinder has a volume of 4 • 3 = 12 cm3. V = 36 • 3 = 108 cm3 By tripling the radius, you would increase the volume nine times. Additional Example 2B: Exploring the Effects of Changing Dimensions A juice can has a radius of 2 in. and a height of 5 in. Explain whether tripling the height of the can would have the same effect on the volume as tripling the radius. By tripling the height, you would triple the volume. By tripling the radius, you would increase the volume to nine times the original. 02/25/10 Changing Dimensions #16 LT: I will describe how increasing or decreasing a measurement will affect area and volume. Predict: What affect will tripling the radius or height have on the volume of a cone? Today’s Plan: -Warm up and Correct Homework -Changing Dimensions -Assignment LT: I will describe how increasing or decreasing a measurement will affect area and volume. Additional Example 2: Exploring the Effects of Changing Dimensions A cone has a radius of 3 ft. and a height of 4 ft. Explain whether tripling the height would have the same effect on the volume of the cone as tripling the radius. When the height of the cone is tripled, the volume is tripled. When the radius is tripled, the volume becomes 9 times the original volume. Try This: Example 2 A cone has a radius of 2 m and a height of 5 m. Explain whether doubling the height would have the same effect on the volume of the cone as doubling the radius. Original Dimensions V= = 1 3 1 3 r2h (22)5 20.93 m3 Double the Height V= = 1 3 1 3 r2 (2h) (22)(2•5) 41.87 m3 Double the Radius V= = 1 3 1 3 (2r)2h (2 • 2)2(5) 83.73 m3 When the height of a cone is doubled, the volume is doubled. When the radius is doubled the volume is 4 times the original volume. Lesson Quiz: Part 2 Find the volume of each figure to the nearest tenth.Use 3.14 for . 3. Explain whether tripling the height of a square pyramid would triple the volume. Yes; the volume is one-third the product of the base area and the height. So if you triple the height, the product would be tripled. 04/26/11 Changing Dimensions LT: I will describe how increasing or decreasing a measurement will affect area and volume. What about Surface Area? Predict: What affect will tripling the radius or height have on the surface area of a cylinder? Today’s Plan: -Warm up -Changing Dimensions -Assignment LT: I will describe how increasing or decreasing a measurement will affect area and volume. Additional Example 2: Exploring the Effects of Changing Dimensions A cylinder has diameter 8 in. and height 3 in. Explain whether tripling the height would have the same effect on the surface area as tripling the radius. They would not have the same effect. Tripling the radius would increase the surface area more than tripling the height. 04/26/11 Changing Dimensions LT: I will describe how increasing or decreasing a measurement will affect area and volume. Assignment: pg 494 #1-3,5-7,9 Today’s Plan: -Warm up -Changing Dimensions -Assignment LT: I will describe how increasing or decreasing a measurement will affect area and volume.