2. Date: 12.4 Notes: Volumes of Prisms and Cylinders Lesson Objective: Find volumes of prisms and cylinders. CCSS: G.GMD.1, 3 You will need: ruler, calculator Real-World App: What is the volume of a soda can? This is Jeopardy!!!: This is 5 the area of the triangle. 9

3. Lesson 1: Volume Volume: The number of non-over­lap­ping unit cubes that will fill the in­te­rior. Prism or Cylinder Volume: V = Bh, where B = base area, B, and h = vertical or | height. Cube Volume: V = s 3

4. Lesson 1: Volume Different Base Areas, B: Rectangle: bh Triangle: ½bh Circle: πr² Regular Polygon: (½as)n, where a = apothem or height of Δ, s = side length, and n = number of sides

5. Lesson 2: What’s the Diff? Measure the 2 different prisms and draw the 3-D figures below. Start by drawing 2 congruent rectangles as shown.

6. Lesson 2: What’s the Diff? Connect each corresponding vertex. Put the length, width and height measures along the sides. 3.5” 1” 2” 3.5” 2” 4”

7. Lesson 2: What’s the Diff? Fill the peach prism to the top with cereal. Carefully pour the cereal into the yellow prism. What do you notice? 3.5” 1” 2” 3.5” 2” 4”

8. Lesson 2: What’s the Diff? Volume of peach prism: Volume of yellow prism: 3.5” 1” 2” 3.5” 2” 4”

9. Lesson 3: Finding Volume Find the volume of the prism. A.A pentagonal prism with side lengths 8 ft and height 12 ft. 8 12

10. Lesson 3: Find the volume. Find the volume of the prism. A.A pentagonal prism with side lengths 8 ft and height 12 ft. 8 12

11. Lesson 3: Find the volume. B.Find the volume of the triangular prism.

12. Lesson 3: Find the volume. C.Find the volume of soda can.

13. Lesson 4: Oblique Solids Cavalieri’s Principle: If 2 solids have the same height, h, and the same cross- sectional area, B, at every level, then they have the same volume. Right Oblique Prism Prism

14. Lesson 4: Oblique Solids

15. 12.4: Do I Get It? Yes or No Find the volume. 1. 2. 3. 4.An oblique cylinder with radius 5’ and height 3’. Round to nearest tenth.