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Warm Up 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. - PowerPoint PPT Presentation
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Holt Geometry
10-8 Spheres
Warm UpFind 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
Holt Geometry
10-8 Spheres
10-8 Spheres
Holt Geometry
Holt Geometry
10-8 Spheres
A sphere is the locus 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
Holt Geometry
10-8 Spheres
Holt Geometry
10-8 Spheres
Example 1A: Finding Volumes of Spheres
Find the volume of the sphere. Give your answer in terms of .
= 2304 in3 Simplify.
Volume of a sphere.
Holt Geometry
10-8 Spheres
Example 1B: Finding Volumes of Spheres
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.
Holt Geometry
10-8 Spheres
Example 2: Sports Application
A sporting goods store sells exercise balls in two sizes, standard (22-in. diameter) and jumbo (34-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 3.7 times as great in volume as a standard ball.
Holt Geometry
10-8 Spheres
Holt Geometry
10-8 Spheres
Example 3A: Finding Surface Area of Spheres
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
Holt Geometry
10-8 Spheres
Example 3C: Finding Surface Area of Spheres
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
Holt Geometry
10-8 Spheres
Example 5: Finding Surface Areas and Volumes of Composite Figures
Find the surface area and volume of the composite figure. Give your answer in terms of .
Step 1 Find the surface area of the composite figure.
The surface area of the composite figure is the sum of the curved surface area of the hemisphere, the lateral area of the cylinder, and the base area of the cylinder.
Holt Geometry
10-8 Spheres
Check It Out! Example 5
Find the surface area and volume of the composite figure.
Step 1 Find the surface area of the composite figure.
The surface area of the composite figure is the sum of the curved surface area of the hemisphere, the lateral area of the cylinder, and the base area of the cylinder.
Holt Geometry
10-8 Spheres
Lesson Quiz: Part I
Find each measurement. Give your answers in terms of .
1. the volume and surface areaof the sphere
2. the volume and surface area of a sphere with great circle area 36 in2
3. the volume and surface areaof the hemisphere
V = 36 cm3; S = 36 cm2
V = 288 in3;S = 144 in2
V = 23,958 ft3;S = 3267 ft2
Holt Geometry
10-8 Spheres
Lesson Quiz: Part II
4. A sphere has radius 4. If the radius is multiplied
by 5, describe what happens to the surface area.
5. Find the volume and surface area of the
composite figure. Give your answer in terms of .
The surface area is multiplied by 25.
V = 522 ft3; S = 267 ft2