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9-2 Volume of Prisms and Cylinders

Geogebra Volume of a Rectangular Prism Using Cubes Volume of a Rectangular Prism Using Cubes (AVolume of a Rectangular Prism Using Cubes (A) Volume of a Prism Volume of a Triangular Prism Volume of a Cylinder Volume of a Cylinder (2) Multiple Volume Problems Volume of a Cylinder (3)

9-2 Videos Find the volume of a cylinder In this lesson you will learn to find the volume of a cylinder by developing and using the cylinder volume formula. Standards: 8.G.C.9 Develop and apply the formula for volume of a cylinder In this lesson you will learn how to develop and apply the formula for volume of a cylinder by using the concept of stacking circles. Standards: 8.G.C.9

Video Tutor Help Volume of a solid Finding the volumes of prismsFinding the volumes of prisms (9-2) Finding the volumes of cylindersFinding the volumes of cylinders (9-2) Volume of Prisms Volume of a Cylinder Khan Academy

Write equations to represent right triangles using the Pythagorean Th... In this lesson you will learn how to write equations to represent right triangles by applying the Pythagorean Theorem. Standards: 8.G.B.7 Solve for unknown side lengths using the Pythagorean Theorem In this lesson you will learn how to solve for unknown side lengths of right triangles by using substitution with the Pythagorean Theorem. Standards: 8.G.B.7 Solve for diagonals in rectangular prisms by applying the Pythagorean... In this lesson you will learn how to solve for diagonal lengths in rectangular prisms by applying the Pythagorean Theorem. Standards: 8.G.B.7

Prove the Pythagorean Theorem using squares and triangles In this lesson you will learn how to prove the Pythagorean Theorem by using squares and triangles. Standards: 8.G.B.6 Use the Pythagorean Theorem to see if a triangle is a right triangle In this lesson, you will learn how to classify a triangle by using the Pythagorean Theorem. Standards: 8.G.B.6 Find the length of the hypotenuse of a right triangle using the Pytha... In this lesson you will learn how to find the length of the hypotenuse of a right triangle by using the Pythagorean Theorem. Standards: 8.G.B.7 Find the length of a leg of a right triangle In this lesson, you will learn how to find the length of a leg of a right triangle by using the Pythagorean Theorem. Standards: 8.G.B.7 Apply the Pythagorean Theorem to three dimensional figures using righ... In this lesson you will learn how to apply the Pythagorean Theorem to three dimensional figures by creating right triangles. Standards: 8.G.B.7

Find the volume of a cylinder In this lesson you will learn to find the volume of a cylinder by developing and using the cylinder volume formula. Standards: 8.G.C.9 Find the volume of a cone In this lesson you will learn to find the volume of a cone by comparing it to the volume of a cylinder. Standards: 8.G.C.9 Find the volume of a sphere In this lesson you will learn to find the volume of a sphere by comparing it to the volume of a cylinder. Standards: 8.G.C.9

Develop and apply the formula for volume of a cylinder In this lesson you will learn how to develop and apply the formula for volume of a cylinder by using the concept of stacking circles. Standards: 8.G.C.9 Develop and apply the formula for volume of a cone In this lesson you will learn how to develop and apply the formula for volume of a cone by comparing cones to cylinders. Standards: 8.G.C.9 Develop and apply the formula for volume of a sphere In this lesson you will learn how to develop and apply the formula for volume of a sphere by comparing spheres and cylinders with similar dimensions. Standards: 8.G.C.9

Video Tutor Help Naming a three-dimensional figure Finding the volumes of prisms Finding the volumes of cylinders Finding the volume of cones Finding the volume of pyramids Finding surface areas of spheres using a formula Finding the volumes of spheres Finding the surface area and volume of similar solid

Worksheets Daily Notetaking Guide Worksheets Version A Practice, Guided Problem Solving Lesson 9-2 Practice 9-2 Guided Problem Solving 9-2

Vocabulary Practice Vocabulary 9A: Graphic Organizer Vocabulary 9B: Reading Comprehension Vocabulary 9C: Reading/Writing Math Symbols Vocabulary 9D: Visual Vocabulary Practice Vocabulary 9E: Vocabulary C Vocabulary 9F: Vocabulary Review Puzzle Vocabulary (Electronic) Flash Cards

Additional Lesson Examples Step-by-Step Examples Lesson 9-2

Lesson Readiness Lesson Quiz Problem of the Day Lesson 9-2

Volume of a Rectangular Prism Using Cubes Volume of a Rectangular Prism Using Cubes (AVolume of a Rectangular Prism Using Cubes (A) Volume of a Prism Multiple Volume Problems

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 . 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. 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.

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 5-2a 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 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 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

Find the volume of this prism. Volumes of Prisms and Cylinders LESSON 9-2 Step 1 Find the area of the base. The area of the base is 3.5 cm 2. B = bhUse the triangle area formula = 3.5Multiply. Substitute 3.5 for b. For h, substitute 2, the height of the triangle = Additional Examples

(continued) Volumes of Prisms and Cylinders LESSON 9-2 Step 2 Use the base area to find the volume. The volume of the prism is 14 cm 3. = Substitute 3.5 for B. For h, substitute 4, the height of the prism. V = BhUse the prism volume formula. = 14Multiply. Additional Examples

Volume of a Cylinder Volume of a Cylinder (2)Volume of a Cylinder (3) Multiple Volume Problems

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.

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.

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 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

Find the volume of the cylinder to the nearest cubic unit. Volumes of Prisms and Cylinders LESSON 9-2 Step 1 Find the area of the base. area of a circle B = r 2 Substitute.= (20 2 ) Estimate Use 3 for π. The area of the base is about 3 x 20² m², or 1200 m². The volume is about 1200 x 12 m³, or 14,400 m³. Simplify. = 400 Additional Examples

Volumes of Prisms and Cylinders LESSON 9-2 Step 2Use the base area to find the volume. volume of a cylinder V = Bh The volume of the cylinder is about 15,080 m³. (continued) Use a calculator. Substitute 400 π for B and 12 for h. = Simplify.= 4800 Additional Examples

Example 5-5a TOYS A wooden block has a single hole drilled entirely through it. What is the volume of the block? Round to the nearest hundredth. The block is a rectangular prism with a cylindrical hole. To find the volume of the block, subtract the volume of the cylinder from the volume of the prism. Find the Volume of a Complex Solid

Example 5-5b Rectangular Prism Cylinder or 72 Answer: The volume of the box is about cubic centimeters.

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.

Find the volume of the the barn. Volume of barn Volume of rectangular prism Volume of triangular prism + = = 30, ,000 V = (40)(50)(15) + (40)(10)(50) 1212 = 40,000 ft 3 The volume of the barn is 40,000 ft 3. Additional Example 4: Finding the Volume of Composite Figures

Partner Share! Example 4 Find the volume of the play house. 3 ft 4 ft 8 ft 5 ft V = (8)(3)(4) + (5)(8)(3) 1212 = V = 156 ft 3 Volume of house Volume of rectangular prism Volume of triangular prism + = The volume of the play house is 156 ft 3.