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
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
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
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.
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”
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”
Lesson 2: What’s the Diff? Volume of peach prism: Volume of yellow prism: 3.5” 1” 2” 3.5” 2” 4”
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
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
Lesson 3: Find the volume. B.Find the volume of the triangular prism.
Lesson 3: Find the volume. C.Find the volume of soda can.
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
Lesson 4: Oblique Solids
12.4: Do I Get It? Yes or No Find the volume An oblique cylinder with radius 5’ and height 3’. Round to nearest tenth.