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

• • Pharmacists Plumber Carpenter Biologist Painters Grocers Chemists Engineers • Gas Station

• Volume – The amount of space contained inside a solid. Measured as

• The volume of a cube is the cube of the length of

• The volume V of a prism is V = Bh, where B

• As a group, agree upon the volume of a stack of computer

• What fills up this volume If you knew how many pages were

• What happens when we slant the stack? Has the volume changed? Has

• If two solids have the same height and the same cross-sectional area

• Based on your knowledge of the volume of a prism, what is

• The volume V of a cylinder is V = Bh = πr

• Pages 547 – 550 • 2 – 12 even, 17, 26, 33,

• Pages 547 – 550 • 2 – 12 even, 17, 26, 30,

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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

Sample Problems

2061. 2 3 cm

540 3 in

477. 5 3 cm

378

144 3 in

62. 35 3 m

12 3 ft

520 3 ft

140. 3 3 in

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