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Volumes of Prisms and Cylinders

Volumes of Prisms and Cylinders. Lesson 11-4. Lesson Quiz. Find the volume of each figure to the nearest whole number. 1. 2. 3. 4. 5. 62 m 3. 1800 ft 3. 45 in. 3. 63 m 3. 1800 mm 3. 11-5. Volumes of Pyramids and Cones. Lesson 11-5. Check Skills You’ll Need.

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Volumes of Prisms and Cylinders

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  1. Volumes of Prisms and Cylinders Lesson 11-4 Lesson Quiz Find the volume of each figure to the nearest whole number. 1. 2. 3. 4.5. 62 m3 1800 ft3 45 in.3 63 m3 1800 mm3 11-5

  2. Volumes of Pyramids and Cones Lesson 11-5 Check Skills You’ll Need (For help, go to Lesson 8-1.) Use the Pythagorean Theorem to find the value of the variable. 1. 2. 3. 8 in. 2.5 m 12 cm Check Skills You’ll Need 11-5

  3. Volumes of Pyramids and Cones Lesson 11-5 Notes The volume of a pyramid is related to the volume of a prism with the same base and height. The relationship can be verified by dividing a cube into three congruent square pyramids, as shown. 11-5

  4. Volumes of Pyramids and Cones Lesson 11-5 Notes The square pyramids are congruent, so they have the same volume. The volume of each pyramid is one third the volume of the cube. 11-5

  5. Volumes of Pyramids and Cones Lesson 11-5 Notes 11-5

  6. 1 3 1 3 V=BhUse the formula for volume of a pyramid. = (225)(22) Substitute 225 for B and 22 for h. Volumes of Pyramids and Cones Lesson 11-5 Additional Examples Real-World Connection Find the volume of a square pyramid with base edges 15 cm and height 22 cm. Because the base is a square, B= 15 • 15 = 225. = 1650 Simplify. The volume of the square pyramid is 1650 cm3. Quick Check 11-5

  7. Volumes of Pyramids and Cones Lesson 11-5 Additional Examples Finding Volume of a Pyramid Find the volume of a square pyramid with base edges 16 m and slant height 17 m. The altitude of a right square pyramid intersects the base at the center of the square. 11-5

  8. Because each side of the square base is 16 m, the leg of the right triangle along the base is 8 m, as shown below. 172= 82h2Use the Pythagorean Theorem. 289 = 64 h2Simplify. Volumes of Pyramids and Cones Lesson 11-5 Additional Examples (continued) Step 1: Find the height of the pyramid. 225 =h2Subtract 64 from each side. h= 15 Find the square root of each side. 11-5

  9. 1 3 1 3 V=BhUse the formula for the volume of a pyramid. = (16  16)15Substitute. Volumes of Pyramids and Cones Lesson 11-5 Additional Examples (continued) Step 2: Find the volume of the pyramid. = 1280 Simplify. The volume of the square pyramid is 1280 m3. Quick Check 11-5

  10. Find the volume of the cone below in terms of . 1 2 r= d = 3 in. 1 3 V=r 2hUse the formula for volume of a cone. 1 3 = (32)(11) Substitute 3 for r and 11 for h. = 33 Simplify. The volume of the cone is 33 in.3. Volumes of Pyramids and Cones Lesson 11-5 Additional Examples Finding Volume of an Oblique Cone Quick Check 11-5

  11. 1 3 d 2 V= r 2h Use the formula for the volume of a cone. r= = 2 1 3 V= (22)(7)Substitute 2 for r and 7 for h. 29.321531Use a calculator. Volumes of Pyramids and Cones Lesson 11-5 Additional Examples Real-World Connection An ice cream cone is 7 cm tall and 4 cm in diameter. About how much ice cream can fit entirely inside the cone? Find the volume to the nearest whole number. About 29 cm3 of ice cream can fit entirely inside the cone. Quick Check 11-5

  12. Volumes of Pyramids and Cones Lesson 11-5 Notes 11-5

  13. Volumes of Pyramids and Cones Lesson 11-5 Notes 11-5

  14. 1470 mm3 3 m3 Volumes of Pyramids and Cones Lesson 11-5 Lesson Quiz Find the volume of each figure. When appropriate, leave your answer in terms of . 1.2. 3. square pyramid with base edges 24 in. long and slant height 15 in. 4. cone with diameter 3 m and height 4 m 5. 60 ft3 1728 in.3 150 ft3 11-5

  15. Volumes of Pyramids and Cones Lesson 11-5 Check Skills You’ll Need Solutions 1. a2 + b2 = c2h2 + (9)2 = (15)2 h2 + 81 = 225h2 = 225 – 81 = 144 h = 144 = 12 cm 2. One leg is half the length of the side of the base, 6 in. a2 + b2 = c2h2 + (6)2 = (10)2h2 + 36 = 100 h = 64 = 8 in. 3. a2 + b2 = c2 (2)2 + (1.5)2 = 2 4 + 2.25 = 2 2 = 6.252 = 6.25 = 2.5 m 11-5

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