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Find each measurement. 1. the radius of circle M if the diameter is 25 cm

Warm Ups. Find each measurement. 1. the radius of circle M if the diameter is 25 cm 2. the circumference of circle X if the radius is 42.5 in. 3. the area of circle T if the diameter is 26 ft 4. the circumference of circle N if the area is 625  cm 2. 12.5 cm. 85  in.

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Find each measurement. 1. the radius of circle M if the diameter is 25 cm

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  1. Warm Ups Find each measurement. 1.the radius of circle M if the diameter is 25 cm 2. the circumference of circle X if the radius is 42.5 in. 3. the area of circle T if the diameter is 26 ft 4. the circumference of circle N if the area is 625 cm2 12.5 cm 85 in. 169 ft2 50cm

  2. Surface Area and Volume of Spheres How do we find the surface area and volume of a sphere? Saturday, October 25, 2014 Lesson 6.9 M2 Unit 3: Day 12

  3. Vocabulary sphere center of a sphere radius of a sphere hemisphere great circle

  4. A sphere is the set of points in space that are a fixed distance from a given point called the center of a sphere. A radius of a sphere connects the center of the sphere to any point on the sphere. A hemisphere is half of a sphere. A great circle divides a sphere into two hemispheres

  5. Vocabulary Great Circle – The intersection of a sphere and a plane that contains the center of the sphere. Hemisphere – half of a sphere, formed when a great circle separates a sphere into two congruent halves.

  6. Find the surface area of the sphere. ANSWER The surface area of the sphere is about 804.25square inches. EXAMPLE Find the surface area of a sphere SOLUTION S = 4πr2 Formula for surface area of a sphere. = 4π(82) Substitute 8 for r. = 256π Simplify. ≈ 804.25 Use a calculator.

  7. The diameter of the sphere is2r = 2 2.25 = 4.5 centimeters. ANSWER The correct answer is B. EXAMPLE 2 Standardized Test Practice S = 4πr2 Formula for surface area of a sphere. SOLUTION 20.25π = 4πr2 Substitute 20.25πfor S. 5.0625 = r2 Divide each side by 4π. 2.25 = r Find the positive square root.

  8. Guided Practice Finding Surface Area of Spheres 1. Find the surface area of a sphere with diameter 76 cm. Give your answers in terms of . S = 4r2 Surface area of a sphere S = 4(38)2 = 5776 cm2

  9. Guided Practice Finding Surface Area of Spheres 2. Find the surface area of a sphere with a great circle that has an area of 49 mi2. A = r2 Area of a circle Substitute 49 for A. 49 = r2 r = 7 Solve for r. S = 4r2 = 4(7)2 = 196 mi2 Substitute 7 for r.

  10. Guided Practice 3. Find the surface area of the sphere. S = 4r2 Surface area of a sphere S = 4(25)2 Substitute 25 for r. S = 2500 cm2

  11. ANSWER The surface area of the sphere is about 5026.55feet2 GUIDED PRACTICE Guided Practice 4. The diameter of a sphere is 40feet. Find the surface area of the sphere. S = 4πr2 Formula for surface area of a sphere. = 4πr(20)2 Substitute 20 for r. = 5026.55 Use a calculator. = 1600π

  12. GUIDED PRACTICE Guided Practice 5. The surface area of a sphere is 30π square meters. Find the radius of the sphere. S = 4πr2 Formula for surface area of a sphere. 30π = 4πr2 Substitute 30πfor S. 7.5 = r2 Divide each side by 4π. 2.74 = r Find the positive square root.

  13. In a sport called sphereing, a person rolls down a hill inside an inflatable ball surrounded by another ball. The diameter of the outer ball is 12feet. Find the surface area of the outer ball. The surface area of the outer ball is 144π, or about 452.39 square feet. ANSWER The diameter of the outer sphere is 12feet, so the 12 radius is = 6feet. 2 EXAMPLE 3 Guided Practice Use the circumference of a sphere 6. EXTREME SPORTS SOLUTION Use the formula for the surface area of a sphere. S = 4πr2 = 4π(62) = 144π

  14. The soccer ball has a diameter of 9 inches. Find its volume. The volume of the soccer ball is 121.5π, or about 381.70 cubic inches. ANSWER The diameter of the ball is 9 inches, so the radius is = 4.5 inches. 9 2 4 V = πr3 3 4 = π(4.5)3 3 EXAMPLE 4 EXAMPLE Find the volume of a sphere SOLUTION Formula for volume of a sphere Substitute. = 121.5π Simplify. Use a calculator. ≈ 381.70

  15. Guided Practice Finding Volumes of Spheres 7. Find the volume of the sphere. Give your answer in terms of . Volume of a sphere. = 2304 in3 Simplify.

  16. Guided Practice Finding Volumes of Spheres 8. Find the diameter of a sphere with volume 36,000 cm3. Volume of a sphere. Substitute 36,000 for V. 27,000 = r3 r = 30 Take the cube root of both sides. d = 60 cm d = 2r

  17. Guided Practice 9. Find the radius of a sphere with volume 2304ft3. Volume of a sphere Substitute for V. r = 12 ft Simplify.

  18. Guided Practice 10. Find the volume of a sphere with surface area 324 in2. Give your answers in terms of . S = 4r2 Surface area of a sphere Substitute 324 for S. 324 = 4r2 r = 9 Solve for r. Substitute 9 for r. The volume of the sphere is 972 in3.

  19. Guided Practice Finding Volumes of Spheres 11. Find the volume of the hemisphere. Volume of a hemisphere Substitute 15 for r. = 2250 m3 Simplify.

  20. EXAMPLE Exploring Effects of Changing Dimensions The radius of the sphere is divided by 3. Describe the effect on the surface area. original dimensions: dimensions divided by 3: S = 4r2 S = 4r2 = 4(3)2 = 36 m3 = 4(1)2 = 4 m3 The surface area is divided by 9.

  21. Guided Practice 12. Exploring Effects of Changing Dimensions Sports Application A sporting goods store sells exercise balls in two sizes, standard (12-in. diameter) and jumbo (36-in. diameter). How many times as great is the volume of a jumbo ball as the volume of a standard ball? standard ball: jumbo ball: A jumbo ball is about (3)3 = 27 times as great in volume as a standard ball.

  22. Homework 239 # 2 – 16 even.17,18

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