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7-3 Volume of Prisms and Cylinders

Geogebra Volume of a Triangular Prism Volume of a Rectangular Prism Volume of a Cylinder Volume of a Rectangular Prism Proof Volume of a Cylinder Multiple Volumes Problems Volume of a Cylinder (2)

Video Tutor Help Naming a three-dimensional figure Drawing a net Finding surface areas of prisms using a net Finding surface areas of cylinders using a net Finding the volumes of prisms Finding the volumes of cylinders

Find surface area of cubes and prisms by pulling them apart Lesson Slides Find surface area of cubes and prisms using formulas Lesson Slides Find missing dimensions using the volume formula Lesson Slides Choose the appropriate measurement for solving a problem Lesson Slides 7-3 Videos

Video Tutor Help Finding the volumes of prismsFinding the volumes of prisms (7-3) Finding the volumes of cylindersFinding the volumes of cylinders (7-3) Finding the Volume of a Rectangular Prism Finding the Volume of a Triangular Prism Finding the Volume of a Cylinder Khan Academy Find the volume of the solid

Worksheets Daily Notetaking Guide Worksheets Version A Practice, Guided Problem Solving Lesson 7-3 Practice 7-3 Guided Problem Solving 7-3

Vocabulary Practice Vocabulary 7A: Graphic Organizer Vocabulary 7B: Reading Comprehension Vocabulary 7C: Reading/Writing Math Symbols Vocabulary 7D: Visual Vocabulary Practice Vocabulary 7E: Vocabulary C Vocabulary 7F: Vocabulary Review Puzzle Vocabulary (Electronic) Flash Cards Geometry

Additional Lesson Examples Step-by-Step Examples Lesson 7-3

Lesson Readiness Lesson Quiz Problem of the Day Lesson 7-3

Multiple Volumes Problems

Volume of a Rectangular Prism Volume of a Rectangular Prism Proof

The volume of a three-dimensional figure is the number of cubes it can hold. Each cube represents a unit of measure called a cubic unit or unit 3.

Height Triangular prism Rectangular prism Cylinder Base Height Base Height Base

Find the volume of each figure to the nearest tenth. A. Additional Example 1: Finding the Volume of Prisms and Cylinders = 192 ft 3 B = 4 12 = 48 ft 2 V = Bh = 48 4 The base is a rectangle. Volume of a prism Substitute for B and h. Multiply.

Find the volume of the figure to the nearest tenth. Use 3.14 for . B. = 192 in 3 B = (4 2 ) = 16 in 2 V = Bh = 16 12 Additional Example 1: Finding the Volume of Prisms and Cylinders The base is a circle. Volume of a cylinder Substitute for B and h. Multiply. Volume of a Cylinder Volume of a Cylinder (2)

Find the volume of the figure to the nearest tenth. Use 3.14 for . C. 7 ft V = Bh = 15 7 = 105 ft 3 B = 6 5 = 15 ft Additional Example 1: Finding the Volume of Prisms and Cylinders The base is a triangle. Volume of a prism Substitute for B and h. Multiply. Volume of a Triangular Prism

Find the volume of the figure to the nearest tenth. Use 3.14 for . A. = 180 in 3 B = 6 3 = 18 in. 2 V = Bh = The base is a rectangle. Volume of prism Partner Share! Example 1 Substitute for B and h. Multiply. 10 in. 6 in. 3 in.

Find the volume of the figure to the nearest tenth. Use 3.14 for . B. 8 cm 15 cm B = (8 2 ) = 64 cm 2 = (64)(15) = 960  3,014.4 cm 3 Partner Share! Example 1 The base is a circle. Volume of a cylinder V = Bh Substitute for B and h. Multiply.

Find the volume of the figure to the nearest tenth. C. 10 ft 14 ft 12 ft = 60 ft 2 = 60(14) = 840 ft 3 Partner Share! Example 1 The base is a triangle. Volume of a prism B = V = Bh Substitute for B and h. Multiply.

A juice box measures 3 in. by 2 in. by 4 in. Explain whether tripling only the length, width, or height of the box would triple the amount of juice the box holds. Additional Example 2A: Exploring the Effects of Changing Dimensions The original box has a volume of 24 in 3. You could triple the volume to 72 in 3 by tripling any one of the dimensions. So tripling the length, width, or height would triple the amount of juice the box holds.

A juice can has a radius of 2 in. and a height of 5 in. Explain whether tripling only the height of the can would have the same effect on the volume as tripling the radius. Additional Example 2B: Exploring the Effects of Changing Dimensions By tripling the height, you would triple the volume. By tripling the radius, you would increase the volume to 9 times the original volume.

A box measures 5 in. by 3 in. by 7 in. Explain whether tripling only the length, width, or height of the box would triple the volume of the box. Partner Share! Example 2A Tripling the length would triple the volume. V = (15)(3)(7) = 315 cm 3 The original box has a volume of (5)(3)(7) = 105 cm 3.

Partner Share! Example 2A Continued The original box has a volume of (5)(3)(7) = 105 cm 3. Tripling the height would triple the volume. V = (5)(3)(21) = 315 cm 3

Partner Share! Example 2A Continued Tripling the width would triple the volume. V = (5)(9)(7) = 315 cm 3 The original box has a volume of (5)(3)(7) = 105 cm 3.

By tripling the radius, you would increase the volume nine times. A cylinder measures 3 cm tall with a radius of 2 cm. Explain whether tripling only the radius or height of the cylinder would triple the amount of volume. Partner Share! Example 2B V = 36 3 = 108 cm 3 The original cylinder has a volume of 4 3 = 12 cm 3.

Partner Share! Example 2B Continued Tripling the height would triple the volume. V = 4 9 = 36 cm 3 The original cylinder has a volume of 4 3 = 12 cm 3.

A drum company advertises a snare drum that is 4 inches high and 12 inches in diameter. Estimate the volume of the drum. Additional Example 3: Music Application d = 12, h = 4 r = = = 6 Volume of a cylinder d2d2 V = (r 2 )h 12 2 = (3.14)(6) 2 4 = (3.14)(36)(4) = ≈ 452 Use 3.14 for . The volume of the drum is approximately 452 in 3.

A drum company advertises a bass drum that is 12 inches high and 28 inches in diameter. Estimate the volume of the drum. Partner Share! Example 3 d = 28, h = 12 r = = = 14 Volume of a cylinder d2d2 V = (r 2 )h 28 2 = (3.14)(14) 2 12 = (3.14)(196)(12) = ≈ 7,385 Use 3.14 for . The volume of the drum is approximately 7,385 in 3.

Example 2-1a Find the volume of the prism. Formula for volume of a prism The base is a rectangle, so Simplify. Answer:The volume is 3200 cubic centimeters. Volume of a Rectangular Prism

Example 5-1a Find the volume of the prism. Volume of a prism The base is a rectangle, so. Simplify. Answer: The volume is 385 cubic inches. (B = l * w) Find the Volume of a Rectangular Prism

Example 5-1b Find the volume of the prism. Answer:

Find the volume of the rectangular prism. LESSON 7-3 V = lwh Use the formula. = (12)(8)(10) Substitute. = 960 Multiply. The volume of the rectangular prism is 960 cm 3. Volumes of Prisms and Cylinders Additional Examples

Example 2-2a Find the volume of the triangular prism. Formula for volume of a prism The height of the prism is 3 in. B = area of base or. Volume of a Triangular Prism

Example 2-2b Simplify. Answer:The volume is 15 cubic inches.

Example 5-2a Find the volume of the prism. Volume of a prism Simplify. Answer: The volume is 270 cubic feet. The base is a triangle, so The height of the prism is 4. (B = ½ bh) Find the Volume of a Triangular Prism

Example 5-2b Find the volume of the prism. Answer:

Find the volume of the triangular prism. LESSON 7-3 V = Bh Use the formula. V = 120 Multiply. The volume of the triangular prism is 120 cm 2. Volumes of Prisms and Cylinders V = (4  10)  6 Substitute Additional Examples

Example 2-5a Find the volume of the cylinder. Round to the nearest tenth. Formula for volume of a cylinder Replace r with 7 and h with 14. Simplify. Answer:The volume is about cubic feet. Volume of a Cylinder

Example 2-5b Find the volume of the cylinder. Round to the nearest tenth. diameter of base 10 m, height 2 m Formula for volume of a cylinder Replace r with 5 and h with 2. Simplify. Answer:The volume is about cubic meters. Since the diameter is 10 m, the radius is 5 m. Volume of a Cylinder

Example 5-3a Find the volume of the cylinder. Round to the nearest tenth. Volume of a cylinder Replace r with 3 and h with 12. Simplify. Answer: The volume is about cubic centimeters. Find the Volumes of Cylinders

Example 5-3b Find the volume of the cylinder. Answer:

Example 5-4a Find the volume of the cylinder. Round to the nearest tenth. diameter of base, 18 yd; height, 25.4 yd Volume of a cylinder Simplify. Replace r with 9 and h with Answer: The volume is about 6,463.5 cubic yards. Since the diameter is 18 yards, the radius is 9 yards. Find the Volumes of Cylinders

Example 5-4b Find the volume of the cylinder. Round to the nearest tenth. diameter of base, 8 yd; height, 10 yd Answer:

Find the volume of the cylinder. Round to the nearest cubic centimeter. LESSON 7-3 The volume of the cylinder is about 113 cm 3. = ( )(2) 2 (9) Substitute Use a calculator.Use the formula. V = r 2 h Volumes of Prisms and Cylinders Additional Examples