# MM2G4 Students will use apply surface area and volume of a sphere. MM2G4 a Use and apply the area and volume of a sphere. MM2G4 b Determine the effect.

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MM2G4 Students will use apply surface area and volume of a sphere. MM2G4 a Use and apply the area and volume of a sphere. MM2G4 b Determine the effect on surface area and volume of changing the radius or diameter of a sphere. 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. 169  ft 2 50  cm Warm Ups

MM2G4 Students will use apply surface area and volume of a sphere. MM2G4 a Use and apply the area and volume of a sphere. MM2G4 b Determine the effect on surface area and volume of changing the radius or diameter of a sphere. Surface Area and Volume of Spheres How do we find the surface area and volume of a sphere? Sunday, August 02, 2015 M2 Unit 3: Day 12 Lesson 6.9

MM2G4 Students will find and compare the measures of a sphere. MM2G4 a Use and apply the area and volume of a sphere. MM2G4 b Determine the effect on surface area and volume of changing the radius or diameter of a sphere. sphere center of a sphere radius of a sphere hemisphere great circle Vocabulary

MM2G4 Students will find and compare the measures of a sphere. MM2G4 a Use and apply the area and volume of a sphere. MM2G4 b Determine the effect on surface area and volume of changing the radius or diameter of a sphere. 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

MM2G4 Students will find and compare the measures of a sphere. MM2G4 a Use and apply the area and volume of a sphere. MM2G4 b Determine the effect on surface area and volume of changing the radius or diameter of a sphere. 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.

MM2G4 Students will find and compare the measures of a sphere. MM2G4 a Use and apply the area and volume of a sphere. MM2G4 b Determine the effect on surface area and volume of changing the radius or diameter of a sphere.

MM2G4 Students will find and compare the measures of a sphere. MM2G4 a Use and apply the area and volume of a sphere. MM2G4 b Determine the effect on surface area and volume of changing the radius or diameter of a sphere. EXAMPLE Find the surface area of a sphere SOLUTION S = 4πr 2 = 4π(8 2 ) = 256π ≈ 804.25 Formula for surface area of a sphere. Substitute 8 for r. Simplify. Use a calculator. Find the surface area of the sphere. The surface area of the sphere is about 804.25 square inches. ANSWER

MM2G4 Students will find and compare the measures of a sphere. MM2G4 a Use and apply the area and volume of a sphere. MM2G4 b Determine the effect on surface area and volume of changing the radius or diameter of a sphere. EXAMPLE 2 Standardized Test Practice SOLUTION S = 4πr 2 20.25π = 4πr 2 5.0625 = r 2 2.25 = r Formula for surface area of a sphere. Substitute 20.25π for S. Divide each side by 4π. Find the positive square root. The diameter of the sphere is 2r = 2 2.25 = 4.5 centimeters. The correct answer is B. ANSWER

MM2G4 Students will find and compare the measures of a sphere. MM2G4 a Use and apply the area and volume of a sphere. MM2G4 b Determine the effect on surface area and volume of changing the radius or diameter of a sphere. 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  r 2 S = 4  (38) 2 = 5776  cm 2 Surface area of a sphere Guided Practice

MM2G4 Students will find and compare the measures of a sphere. MM2G4 a Use and apply the area and volume of a sphere. MM2G4 b Determine the effect on surface area and volume of changing the radius or diameter of a sphere. Finding Surface Area of Spheres 2. Find the surface area of a sphere with a great circle that has an area of 49  mi 2. Substitute 49  for A. 49  =  r 2 r = 7Solve for r. S = 4  r 2 = 4  (7) 2 = 196  mi 2 Substitute 7 for r. A =  r 2 Area of a circle Guided Practice

MM2G4 Students will find and compare the measures of a sphere. MM2G4 a Use and apply the area and volume of a sphere. MM2G4 b Determine the effect on surface area and volume of changing the radius or diameter of a sphere. 3. Find the surface area of the sphere. Substitute 25 for r. S = 2500  cm 2 S = 4  r 2 S = 4  (25) 2 Surface area of a sphere Guided Practice

MM2G4 Students will find and compare the measures of a sphere. MM2G4 a Use and apply the area and volume of a sphere. MM2G4 b Determine the effect on surface area and volume of changing the radius or diameter of a sphere. GUIDED PRACTICE 4. The diameter of a sphere is 40 feet. Find the surface area of the sphere. S = 4πr 2 = 4πr(20) 2 = 5026.55 Formula for surface area of a sphere. Substitute 20 for r. Use a calculator. The surface area of the sphere is about 5026.55 feet 2 ANSWER Guided Practice = 1600π

MM2G4 Students will find and compare the measures of a sphere. MM2G4 a Use and apply the area and volume of a sphere. MM2G4 b Determine the effect on surface area and volume of changing the radius or diameter of a sphere. GUIDED PRACTICE 5. The surface area of a sphere is 30π square meters. Find the radius of the sphere. S = 4πr 2 30π = 4πr 2 7.5 = r 2 2.74 = r Formula for surface area of a sphere. Substitute 30π for S. Divide each side by 4π. Find the positive square root. Guided Practice

MM2G4 Students will find and compare the measures of a sphere. MM2G4 a Use and apply the area and volume of a sphere. MM2G4 b Determine the effect on surface area and volume of changing the radius or diameter of a sphere. EXAMPLE 3 Use the circumference of a sphere 6. EXTREME SPORTS 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 12 feet. Find the surface area of the outer ball. SOLUTION The diameter of the outer sphere is 12 feet, so the radius is = 6 feet. 12 2 Use the formula for the surface area of a sphere. S = 4πr 2 = 4π(6 2 )= 144π The surface area of the outer ball is 144π, or about 452.39 square feet. ANSWER Guided Practice

MM2G4 Students will find and compare the measures of a sphere. MM2G4 a Use and apply the area and volume of a sphere. MM2G4 b Determine the effect on surface area and volume of changing the radius or diameter of a sphere.

MM2G4 Students will find and compare the measures of a sphere. MM2G4 a Use and apply the area and volume of a sphere. MM2G4 b Determine the effect on surface area and volume of changing the radius or diameter of a sphere. EXAMPLE 4 Find the volume of a sphere SOLUTION The soccer ball has a diameter of 9 inches. Find its volume. Formula for volume of a sphere Substitute. V = πr 3 4 3 = π(4.5) 3 4 3 The diameter of the ball is 9 inches, so the radius is = 4.5 inches. 9 2 = 121.5π ≈ 381.70 Simplify. Use a calculator. The volume of the soccer ball is 121.5π, or about 381.70 cubic inches. ANSWER EXAMPLE

MM2G4 Students will find and compare the measures of a sphere. MM2G4 a Use and apply the area and volume of a sphere. MM2G4 b Determine the effect on surface area and volume of changing the radius or diameter of a sphere. Finding Volumes of Spheres 7. Find the volume of the sphere. Give your answer in terms of . = 2304  in 3 Simplify. Volume of a sphere. Guided Practice

MM2G4 Students will find and compare the measures of a sphere. MM2G4 a Use and apply the area and volume of a sphere. MM2G4 b Determine the effect on surface area and volume of changing the radius or diameter of a sphere. Finding Volumes of Spheres 8. Find the diameter of a sphere with volume 36,000  cm 3. Substitute 36,000  for V. 27,000 = r 3 r = 30 d = 60 cmd = 2r Take the cube root of both sides. Volume of a sphere. Guided Practice

MM2G4 Students will find and compare the measures of a sphere. MM2G4 a Use and apply the area and volume of a sphere. MM2G4 b Determine the effect on surface area and volume of changing the radius or diameter of a sphere. 9. Find the radius of a sphere with volume 2304  ft 3. Volume of a sphere Substitute for V. r = 12 ftSimplify. Guided Practice

MM2G4 Students will find and compare the measures of a sphere. MM2G4 a Use and apply the area and volume of a sphere. MM2G4 b Determine the effect on surface area and volume of changing the radius or diameter of a sphere. 10. Find the volume of a sphere with surface area 324  in 2. Give your answers in terms of . Substitute 324  for S. 324  = 4  r 2 r = 9Solve for r. Substitute 9 for r. The volume of the sphere is 972  in 3. S = 4  r 2 Surface area of a sphere Guided Practice

MM2G4 Students will find and compare the measures of a sphere. MM2G4 a Use and apply the area and volume of a sphere. MM2G4 b Determine the effect on surface area and volume of changing the radius or diameter of a sphere. Finding Volumes of Spheres 11. Find the volume of the hemisphere. Volume of a hemisphere Substitute 15 for r. = 2250  m 3 Simplify. Guided Practice

MM2G4 Students will find and compare the measures of a sphere. MM2G4 a Use and apply the area and volume of a sphere. MM2G4 b Determine the effect on surface area and volume of changing the radius or diameter of a sphere. The radius of the sphere is divided by 3. Describe the effect on the surface area. original dimensions:dimensions divided by 3: The surface area is divided by 9. S = 4  r 2 = 4  (3) 2 = 36  m 3 S = 4  r 2 = 4  (1) 2 = 4  m 3 Exploring Effects of Changing Dimensions EXAMPLE

MM2G4 Students will find and compare the measures of a sphere. MM2G4 a Use and apply the area and volume of a sphere. MM2G4 b Determine the effect on surface area and volume of changing the radius or diameter of a sphere. 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. Guided Practice 12. Exploring Effects of Changing Dimensions

MM2G4 Students will find and compare the measures of a sphere. MM2G4 a Use and apply the area and volume of a sphere. MM2G4 b Determine the effect on surface area and volume of changing the radius or diameter of a sphere. Homework 239 # 2 – 16 even.17,18

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