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Volumes of Pyramids and Cones

1470 mm 3. 3 m 3. 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.

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Volumes of Pyramids and Cones

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  1. 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 11-6

  2. 1. A = r 2 = (6)2 = 36 113.1 in.2, C = = 2 (6) = 12 37.7 in. 2. A = r 2 = (5)2 = 25 78.5 cm2, C = = 2 (5) = 10 31.4 cm 3. A = r 2 = (2.5)2 = 6.25 19.6 ft2, C = = 2 (2.5) = 5 15.7 ft 4. A = r 2 = (1.2)2 = 1.44 4.5 m2, C = = 2 (1.2) = 2.4 7.5 m 5. A = r 2 = (15)2 = 225 706.9 yd2, C = = 2 (15) = 30 94.2 yd 2 r 2 r 2 r 2 r 2 r 2 r 6. A = r 2 = (12)2 = 144 452.4 mm2, C = = 2 (12) = 24 75.4 mm Surface Areas and Volumes of Spheres Lesson 11-6 Check Skills You’ll Need (For help, go to Lesson 1-9.) Find the area and circumference of a circle with the given radius. Round your answers to the nearest tenth. 1. 6 in. 2. 5 cm 3. 2.5 ft 4. 1.2 m 5. 15 yd 6. 12 mm Check Skills You’ll Need 11-6

  3. Surface Areas and Volumes of Spheres Lesson 11-6 Notes A sphere is the set of points in space equidistant from a given point called the center. A radius of a sphere is a segment that has one endpoint at the center and the other endpoint on the sphere. A diameter is a segment passing through the center with endpoints on the sphere. 11-6

  4. Surface Areas and Volumes of Spheres Lesson 11-6 Notes A great circle is the intersection of the sphere and a plane passing through the center of the sphere. The circumference of a great circle is the circumference of the sphere. A great circle divides a sphere into two hemispheres. 11-6

  5. Surface Areas and Volumes of Spheres Lesson 11-6 Notes 11-6

  6. Surface Areas and Volumes of Spheres Lesson 11-6 Notes 11-6

  7. S.A. = 4 r 2Use the formula for the surface area of a sphere. 18 2 = 4 • 92Substitute r== 9. = 324 Simplify. The surface area of the sphere is 324 ft2. Surface Areas and Volumes of Spheres Lesson 11-6 Additional Examples Finding Surface Area of a Sphere Find the surface area of the sphere below. Leave your answer in terms of . Quick Check 11-6

  8. Step 1: Use the circumference to find the radius in terms of . C=2 r Use the formula for circumference. 13=2 r Substitute 13 for C. 13 2 13 2 = r Solve for r. S.A. = 4r 2Use the formula for the surface area of a sphere. 13 2 = 4• ( )2Substitute for r. 169 =Simplify. 53.794371Use a calculator. Surface Areas and Volumes of Spheres Lesson 11-6 Additional Examples Real-World Connection Quick Check The circumference of a rubber ball is 13 cm. Calculate its surface area to the nearest whole number. Step 2: Use the radius to find the surface area. To the nearest whole number, the surface area of the rubber ball is 54 cm2. 11-6

  9. 4 3 V= r 3Use the formula for the volume of a sphere. 30 2 4 3 = • 153Substitute r = = 15. = 4500Simplify. The volume of the sphere is 4500 cm3. Surface Areas and Volumes of Spheres Lesson 11-6 Additional Examples Finding Volume Find the volume of the sphere. Leave your answer in terms of . Quick Check 11-6

  10. 4 3 V= r 3Use the formula for the volume of a sphere. 4 3 1= r 3Substitute. 3 3 4 3 4 = r 3Solve for r 3. = r Find the cube root of each side. r0.62035049Use a calculator. Surface Areas and Volumes of Spheres Lesson 11-6 Additional Examples Using Volume to Find Surface Area The volume of a sphere is 1 in.3. Find its surface area to the nearest tenth. Step 1: Use the volume to find the radius r. 11-6

  11. S.A. = 4r 2Use the formula for the surface area of a sphere. 4.8359744Use a calculator. 4(0.62035049)2Substitute. Surface Areas and Volumes of Spheres Lesson 11-6 Additional Examples (continued) Step 2: Use the radius to find the surface area. To the nearest tenth, the surface area of the sphere is 4.8 in.2. Quick Check 11-6

  12. For Exercises 1–3, find the surface area. Leave your answer in terms of . 1. a sphere whose diameter is 13 cm 2. a ball whose circumference is 19 mm 3. a sphere whose volume is 288 in.3 For Exercises 4 and 5, find the volume. Round your answer to the nearest whole number. 4. sphere with radius 5 m 5. sphere with diameter 7 yd 169 cm2 361 mm2 144 in.2 Surface Areas and Volumes of Spheres Lesson 11-6 Lesson Quiz 524 m3 180 yd3 11-6

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