Geometry 4.6 Turn Up the … Day 1

4.6 Using Volume Formulas Objectives Apply the volume formulas for a pyramid, a cylinder, a cone, and a sphere to solve problems

Problem 1: On a Roll Collaborate 1-3 (5 Minutes) 𝐶 𝑐𝑖𝑟𝑐𝑙𝑒 =2𝜋𝑟 3) Determine the radius and the height of each When h = 8.5, C = 11 𝐶=2𝜋𝑟 11=2 3.14 𝑟 11=6.28𝑟 𝑟=1.75 𝑖𝑛𝑐ℎ𝑒𝑠

Problem 1: On a Roll 3) Determine the radius and the height of each When h = 11, C = 8.5 𝐶=2𝜋𝑟 8.5=2 3.14 𝑟 8.5=6.28𝑟 𝑟=1.35 𝑖𝑛𝑐ℎ𝑒𝑠 Collaborate 4-5 (5 Minutes) 𝑉 𝑐𝑦𝑙𝑖𝑛𝑑𝑒𝑟 =𝜋 𝑟 2 ℎ

Problem 1: On a Roll 4) Determine the volume of each cylinder When r = 1.75, h = 8.5 𝑉=𝜋 𝑟 2 ℎ 𝑉=3.14 1.75 2 (8.5) 𝑉=81.74 𝑖𝑛𝑐ℎ𝑒𝑠 3

Problem 1: On a Roll 4) Determine the volume of each cylinder When r = 1.35, h = 11 𝑉=𝜋 𝑟 2 ℎ 𝑉=3.14 1.35 2 (11) 𝑉=62.95 𝑖𝑛𝑐ℎ𝑒𝑠 3

Problem 1: On a Roll Together #6 𝑉=81.74 , ℎ=11 𝑉=𝜋 𝑟 2 ℎ 81.74=3.14 𝑟 2 (11) 81.74=34.54 𝑟 2 𝑟 2 =2.37 𝑟 2 = 2.37 𝑟=1.54 𝑖𝑛𝑐ℎ𝑒𝑠

Problem 2: Let’s Vase It Together 1-2 A possible strategy could be to use cylinders as an approximate shape of the vase

Problem 2: Let’s Vase It Average of the radii 2+3 2 =2.5 𝑖𝑛𝑐ℎ𝑒𝑠 2+4 2 =3 𝑖𝑛𝑐ℎ𝑒𝑠

Problem 3 Balloons, Lakes, and Graphs Collaborate 1 (8 Minutes) Hint: Use the top as a hemisphere: 𝑉= 1 2 4 3 𝜋 𝑟 3 Use the bottom as a cone: 𝑉= 1 3 𝜋 𝑟 2 ℎ Add the volumes together

Problem 3 Balloons, Lakes, and Graphs #1 ℎ 𝑏𝑎𝑙𝑙𝑜𝑜𝑛 =75 𝑓𝑒𝑒𝑡 𝑑 𝑤𝑖𝑑𝑒𝑠𝑡 =55 𝑓𝑒𝑒𝑡 Total Approx Volume = 𝑉 ℎ𝑒𝑚𝑖 + 𝑉 𝑐𝑜𝑛𝑒 =81,133.02 𝑓𝑡 3 r = .5d r = 27.5 hemisphere cone h = 75 – r h = 47.5 Volume of Hemisphere 𝑉= 1 2 𝑥 4 3 𝜋 𝑟 3 𝑉= 2 3 𝑥3.14𝑥 27.5 3 𝑉 ℎ𝑒𝑚𝑖 =43,534.79 𝑓𝑡 3 Volume of Cone 𝑉= 1 3 𝜋 𝑟 2 ℎ 𝑐𝑜𝑛𝑒 𝑉= 1 3 𝑥3.14𝑥 27.5 2 𝑥47.5 𝑉 𝑐𝑜𝑛𝑒 =37,598.23 𝑓𝑡 3

Summarize What does the circumference of the base of a cylinder represent in a rectangle? How can we determine the radius of a cylinder/sphere if we know the diameter of the object? Describe what an approximation is. No Homework Today. Quiz Tomorrow

Geometry 4.6 Turn Up the … Day 2

4.6 Using Volume Formulas Objectives Apply the volume formulas for a pyramid, a cylinder, a cone, and a sphere to solve problems

Problem 3 Balloons, Lakes, and Graphs Collaborate #2 (3 Minutes) Hint: Find the volume of the cone cup only 𝑑=2.75 𝑖𝑛𝑐ℎ𝑒𝑠 𝑟= 2.75 2 =1.375 𝑖𝑛𝑐ℎ𝑒𝑠 ℎ=4 𝑖𝑛𝑐ℎ𝑒𝑠 𝑉= 1 3 (3.14) 1.375 2 (4) 𝑉=7.92 𝑖𝑛𝑐ℎ𝑒𝑠 3

Problem 3 Balloons, Lakes, and Graphs Collaborate #3 (3 Minutes) Hint: Set the volume equations equal 𝑉 𝑠𝑝ℎ𝑒𝑟𝑒 = 4 3 𝜋 𝑟 3 𝑉 𝑐𝑜𝑛𝑒 = 1 3 𝜋 𝑟 2 ℎ 𝑉 𝑠𝑝ℎ𝑒𝑟𝑒 = 𝑉 𝑐𝑜𝑛𝑒 4 3 𝜋 𝑟 3 = 1 3 𝜋 𝑟 2 ℎ Solve for h ℎ=4𝑟

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Formative Assessment Quiz 4.1-4.6 Formative Assessment Skills Practice Use the formulas to answer the multiple choice questions 𝐴 𝑝𝑎𝑟𝑎𝑙𝑙𝑒𝑙𝑜𝑔𝑟𝑎𝑚 =𝑏ℎ 𝐴 𝑡𝑟𝑖𝑎𝑛𝑔𝑙𝑒 = 1 2 𝑏ℎ 𝐴 𝑡𝑟𝑎𝑝𝑒𝑧𝑜𝑖𝑑 = 1 2 𝑏 1 + 𝑏 2 ℎ 𝑉 𝑝𝑟𝑖𝑠𝑚 =𝐵ℎ 𝑉 𝑝𝑦𝑟𝑎𝑚𝑖𝑑 = 1 3 𝐵ℎ When finished with the quiz, Skills Practice 4.6 Pg. 445-451 (1-26) 𝑉 𝑐𝑦𝑙𝑖𝑛𝑑𝑒𝑟 =𝜋 𝑟 2 ℎ 𝑉 𝑐𝑜𝑛𝑒 = 1 3 𝜋 𝑟 2 ℎ 𝑉 𝑠𝑝ℎ𝑒𝑟𝑒 = 4 3 𝜋 𝑟 3