Volume of Prisms and Cylinders Geometry 10 5
- Slides: 47
Volume of Prisms and Cylinders Geometry 10 -5
• 1 question Many, Many Answers Warm-Up Exercises
• So far we have studied length and area, now we are moving into the last topic in geometry, volume • Make a list of occupations that work with quantities that are measured by volume. The longest list wins Volume
Answers
• • Pharmacists Plumber Carpenter Biologist Painters Grocers Chemists Engineers • Gas Station • Blood Mobile Volume
• Volume – The amount of space contained inside a solid. Measured as a cubic. Like m 3 or ft 3 Vocabulary
New Material
• The volume of a cube is the cube of the length of its side, or V=s 3 Volume of a cube
• The volume V of a prism is V = Bh, where B is the area of a base and h is the height Volume of a Prism
Volume of a Prism
• As a group, agree upon the volume of a stack of computer paper Volume Exploration
• What fills up this volume If you knew how many pages were in the stack, could calculate the volume of one piece? Volume Exploration
• What happens when we slant the stack? Has the volume changed? Has the height changed? Volume Exploration
• If two solids have the same height and the same cross-sectional area at every level, then they have the same volume Cavalieri’s Principle
Cavalieri’s Principle
• Based on your knowledge of the volume of a prism, what is the volume of a cylinder? Volume of a Cylinder
• The volume V of a cylinder is V = Bh = πr 2 h where B is the area of a base, h is the height, and r is the radius of a base Regardless of whether or not it is a right cylinder Volume of a Cylinder
• The volume V of a cylinder is V = Bh = πr 2 h where B is the area of a base, h is the height, and r is the radius of a base Volume of a Cylinder
Example
Example
Example
Example
Example
Example
Example
Sample Problems
2061. 2 3 cm
540 3 in
477. 5 3 cm
72
378
64
144 3 in
62. 35 3 m
12 3 ft
520 3 ft
140. 3 3 in
Practice Problems
Practice Problems
Practice Problems
Practice Problems
Practice Problems
Practice Problems
Practice Problems
Practice Problems
• Pages 547 – 550 • 2 – 12 even, 17, 26, 33, 34, 46 Homework
• Pages 547 – 550 • 2 – 12 even, 17, 26, 30, 31, 33, 34, 46 Honors Homework
