1. Geometry
4.6 Turn Up the …
Day 1

2. 4.6 Using Volume Formulas Objectives
Apply the volume formulas for a pyramid, a cylinder, a cone, and a sphere to solve problems

3. 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= 𝑟
11=6.28𝑟
𝑟=1.75 𝑖𝑛𝑐ℎ𝑒𝑠

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

5. 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= (8.5) 𝑉=81.74 𝑖𝑛𝑐ℎ𝑒𝑠 3

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

7. 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

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

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

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

11. Problem 3 Balloons, Lakes, and Graphs#1
ℎ 𝑏𝑎𝑙𝑙𝑜𝑜𝑛 =75 𝑓𝑒𝑒𝑡
𝑑 𝑤𝑖𝑑𝑒𝑠𝑡 =55 𝑓𝑒𝑒𝑡
Total Approx Volume
= 𝑉 ℎ𝑒𝑚𝑖 + 𝑉 𝑐𝑜𝑛𝑒
=81, 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
𝑉 ℎ𝑒𝑚𝑖 =43, 𝑓𝑡 3
Volume of Cone
𝑉= 1 3 𝜋 𝑟 2 ℎ 𝑐𝑜𝑛𝑒
𝑉= 1 3 𝑥3.14𝑥 𝑥47.5
𝑉 𝑐𝑜𝑛𝑒 =37, 𝑓𝑡 3

12. 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

13. Geometry
4.6 Turn Up the …
Day 2

14. 4.6 Using Volume Formulas Objectives
Apply the volume formulas for a pyramid, a cylinder, a cone, and a sphere to solve problems

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

16. Problem 3 Balloons, Lakes, and Graphs
Collaborate #3 (3 Minutes)
Hint: Set the volume equations equal
𝑉 𝑠𝑝ℎ𝑒𝑟𝑒 = 4 3 𝜋 𝑟 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

18. 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 = 𝑏 1 + 𝑏 2 ℎ
𝑉 𝑝𝑟𝑖𝑠𝑚 =𝐵ℎ
𝑉 𝑝𝑦𝑟𝑎𝑚𝑖𝑑 = 1 3 𝐵ℎ
When finished with the quiz, Skills Practice 4.6
Pg (1-26)
𝑉 𝑐𝑦𝑙𝑖𝑛𝑑𝑒𝑟 =𝜋 𝑟 2 ℎ
𝑉 𝑐𝑜𝑛𝑒 = 1 3 𝜋 𝑟 2 ℎ
𝑉 𝑠𝑝ℎ𝑒𝑟𝑒 = 4 3 𝜋 𝑟 3