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8-5

8-5. Volume of Prisms and Cylinders. Warm Up. Problem of the Day. Lesson Presentation. Course 3. 8-5. Volume of Prisms and Cylinders. Course 3. Warm Up Find the area of each figure described. Use 3.14 for p . 1. a triangle with a base of 6 feet and a height of 3 feet

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8-5

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  1. 8-5 Volume of Prisms and Cylinders Warm Up Problem of the Day Lesson Presentation Course 3

  2. 8-5 Volume of Prisms and Cylinders Course 3 Warm Up Find the area of each figure described. Use 3.14 for p. 1. a triangle with a base of 6 feet and a height of 3 feet 2. a circle with radius 5 in. 9 ft2 78.5 ft2

  3. 8-5 Volume of Prisms and Cylinders Course 3 Problem of the Day You are painting identical wooden cubes red and blue. Each cube must have 3 red faces and 3 blue faces. How many cubes can you paint that can be distinguished from one another? only 2

  4. 8-5 Volume of Prisms and Cylinders Course 3 Learn to find the volume of prisms and cylinders.

  5. 8-5 Volume of Prisms and Cylinders Course 3 Insert Lesson Title Here Vocabulary cylinder prism

  6. 8-5 Volume of Prisms and Cylinders Course 3 A cylinder is a three-dimensional figure that has two congruent circular bases. A prism is a three-dimensional figure named for the shape of its bases. The two bases are congruent polygons. All of the other faces are parallelograms.

  7. 8-5 Volume of Prisms and Cylinders Course 3 Rectangular prism Cylinder Triangular prism Height Height Height Base Base Base

  8. 8-5 Volume of Prisms and Cylinders Course 3 VOLUME OF PRISMS AND CYLINDERS B = 2(5) = 10 units2 V = Bh V = 10(3) = 30 units3 B =  (22) V = Bh = 4 units2 = (r2)h V = (4)(6) = 24 75.4 units3

  9. 8-5 Volume of Prisms and Cylinders Remember! Area is measured in square units. Volume is measured in cubic units. Course 3

  10. 8-5 Volume of Prisms and Cylinders Course 3 Additional Example 1A: Finding the Volume of Prisms and Cylinders Find the volume of each figure to the nearest tenth. Use 3.14 for . a rectangular prism with base 2 cm by 5 cm and height 3 cm B = 2 • 5 = 10 cm2 Area of base Volume of a prism V = Bh = 10 • 3 = 30 cm3

  11. 8-5 Volume of Prisms and Cylinders Course 3 Additional Example 1B: Finding the Volume of Prisms and Cylinders Find the volume of the figure to the nearest tenth. Use 3.14 for . B =  (42) = 16in2 Area of base 4 in. Volume of a cylinder V = Bh 12 in. = 16• 12 = 192  602.9 in3

  12. 8-5 Volume of Prisms and Cylinders 1 2 B = • 6 • 5 = 15 ft2 Course 3 Additional Example 1C: Finding the Volume of Prisms and Cylinders Find the volume of the figure to the nearest tenth. Use 3.14 for . Area of base 5 ft V = Bh Volume of a prism = 15 • 7 = 105 ft3 7 ft 6 ft

  13. 8-5 Volume of Prisms and Cylinders Course 3 Check It Out: Example 1A Find the volume of the figure to the nearest tenth. Use 3.14 for . A rectangular prism with base 5 mm by 9 mm and height 6 mm. B = 5 • 9 = 45 mm2 Area of base Volume of prism V = Bh = 45 • 6 = 270 mm3

  14. 8-5 Volume of Prisms and Cylinders Course 3 Check It Out: Example 1B Find the volume of the figure to the nearest tenth. Use 3.14 for . B =  (82) Area of base 8 cm = 64 cm2 Volume of a cylinder V = Bh 15 cm = (64)(15) = 960 3,014.4 cm3

  15. 8-5 Volume of Prisms and Cylinders 1 2 B = • 12 • 10 Course 3 Check It Out: Example 1C Find the volume of the figure to the nearest tenth. Use 3.14 for . Area of base 10 ft = 60 ft2 Volume of a prism V = Bh = 60(14) 14 ft = 840 ft3 12 ft

  16. 8-5 Volume of Prisms and Cylinders Course 3 Additional Example 2A: Exploring the Effects of Changing Dimensions A juice box measures 3 in. by 2 in. by 4 in. Explain whether tripling the length, width, or height of the box would triple the amount of juice the box holds. The original box has a volume of 24 in3. You could triple the volume to 72 in3 by tripling any one of the dimensions. So tripling the length, width, or height would triple the amount of juice the box holds.

  17. 8-5 Volume of Prisms and Cylinders Course 3 Additional Example 2B: Exploring the Effects of Changing Dimensions A juice can has a radius of 2 in. and a height of 5 in. Explain whether tripling the height of the can would have the same effect on the volume as tripling the radius. By tripling the height, you would triple the volume. By tripling the radius, you would increase the volume to nine times the original.

  18. 8-5 Volume of Prisms and Cylinders Course 3 Check It Out: Example 2A A box measures 5 in. by 3 in. by 7 in. Explain whether tripling the length, width, or height of the box would triple the volume of the box. The original box has a volume of (5)(3)(7) = 105 cm3. V = (15)(3)(7) = 315 cm3 Tripling the length would triple the volume.

  19. 8-5 Volume of Prisms and Cylinders Course 3 Check It Out: Example 2A Continued The original box has a volume of (5)(3)(7) = 105 cm3. V = (5)(3)(21) = 315 cm3 Tripling the height would triple the volume.

  20. 8-5 Volume of Prisms and Cylinders Course 3 Check It Out: Example 2A Continued The original box has a volume of (5)(3)(7) = 105 cm3. V = (5)(9)(7) = 315 cm3 Tripling the width would triple the volume.

  21. 8-5 Volume of Prisms and Cylinders Course 3 Check It Out: Example 2B A cylinder measures 3 cm tall with a radius of 2 cm. Explain whether tripling the radius or height of the cylinder would triple the amount of volume. The original cylinder has a volume of 4 • 3 = 12 cm3. V = 36 • 3= 108cm3 By tripling the radius, you would increase the volume nine times.

  22. 8-5 Volume of Prisms and Cylinders Course 3 Check It Out: Example 2B Continued The original cylinder has a volume of 4 • 3 = 12 cm3. V = 4 • 9= 36cm3 Tripling the height would triple the volume.

  23. 8-5 Volume of Prisms and Cylinders Course 3 Additional Example 3: Music Application A drum company advertises a snare drum that is 4 inches high and 12 inches in diameter. Estimate the volume of the drum. d = 12, h = 4 d 2 12 2 r = = = 6 Volume of a cylinder. V = (r2)h = (3.14)(6)2• 4 Use 3.14 for p. = (3.14)(36)(4) = 452.16 ≈ 452 The volume of the drum is approximately 452 in.2

  24. 8-5 Volume of Prisms and Cylinders Course 3 Check It Out: Example 3 A drum company advertises a bass drum that is 12 inches high and 28 inches in diameter. Estimate the volume of the drum. d = 28, h = 12 d 2 28 2 r = = = 14 Volume of a cylinder. V = (r2)h = (3.14)(14)2• 12 Use 3.14 for . = (3.14)(196)(12) = 7385.28 ≈ 7,385 The volume of the drum is approximately 7,385 in.2

  25. 8-5 Volume of Prisms and Cylinders Volume of barn Volume of rectangular prism Volume of triangular prism = + 1 2 V = (40)(50)(15) + (40)(10)(50) Course 3 Additional Example 4: Finding the Volume of Composite Figures Find the volume of the the barn. = 30,000 + 10,000 = 40,000 ft3 The volume is 40,000 ft3.

  26. 8-5 Volume of Prisms and Cylinders Volume of house Volume of rectangular prism Volume of triangular prism 1 2 = = (8)(3)(4) + (5)(8)(3) + Course 3 Check It Out: Example 4 Find the volume of the house. 5 ft = 96 + 60 4 ft V = 156 ft3 8 ft 3 ft

  27. 8-5 Volume of Prisms and Cylinders Course 3 Insert Lesson Title Here Lesson Quiz Find the volume of each figure to the nearest tenth. Use 3.14 for . 10 in. 1. 3. 2 in. 2. 12 in. 12 in. 10.7 in. 15 in. 3 in. 8.5 in. 942 in3 160.5 in3 306 in3 4. Explain whether doubling the radius of the cylinder above will double the volume. No; the volume would be quadrupled because you have to use the square of the radius to find the volume.

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