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 cm2
12.5 cm
85 in.
169 ft2
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?
Thursday, April 20, 2023
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 = 4πr2
= 4π(82)
= 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 squareinches.
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 = 4πr2
20.25π = 4πr2
5.0625 = r2
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 = 4r2
S = 4(38)2 = 5776 cm2
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 mi2.
Substitute 49 for A.49 = r2
r = 7 Solve for r.
S = 4r2
= 4(7)2 = 196 mi2 Substitute 7 for r.
A = r2 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 cm2
S = 4r2
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 = 4πr2
= 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 feet2
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 = 4πr2
30π = 4πr2
7.5 = r2
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
2Use the formula for the surface area of a sphere.
S = 4πr2 = 4π(62) = 144πThe 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 4Find 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 = πr34
3
= π(4.5)343
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 in3 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 cm3.
Substitute 36,000 for V.
27,000 = r3
r = 30
d = 60 cm d = 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 ft3.
Volume of a sphere
Substitute for V.
r = 12 ft 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.
10. Find the volume of a sphere with surface area 324 in2. Give your answers in terms of .
Substitute 324 for S.324 = 4r2
r = 9 Solve for r.
Substitute 9 for r.
The volume of the sphere is 972 in3.
S = 4r2 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 m3 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 = 4r2
= 4(3)2 = 36 m3
S = 4r2
= 4(1)2 = 4 m3
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
34
3V rp=
( )346
3V p=
3288V inp=
34
3V rp=
( )3418
3V p=
37776V inp=
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
Top Related