# 11-4 11-4Spheres Spheres Warm Up Lesson Presentation Lesson

11-4 11-4Spheres Spheres Warm Up Lesson Presentation Lesson Quiz HoltMcDougal GeometryGeometry Holt 11-4 Spheres

Warm Up Find each measurement. 1. the radius of circle M if the diameter is 25 cm 12.5 cm 2. the circumference of circle X if the radius is 42.5 in. 85 in. 3. the area of circle T if the diameter is 26 ft 169 ft2 4. the circumference of circle N if the area is 625 cm2 50 cm Holt McDougal Geometry 11-4 Spheres

Objectives Learn and apply the formula for the volume of a sphere. Learn and apply the formula for the surface area of a sphere. Holt McDougal Geometry 11-4 Spheres Vocabulary sphere

center of a sphere radius of a sphere hemisphere great circle Holt McDougal Geometry 11-4 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 McDougal Geometry 11-4 Spheres Holt McDougal Geometry 11-4 Spheres Example 1A: Finding Volumes of Spheres Find the volume and surface area of the sphere. Give your answer in terms of .

Holt McDougal Geometry 11-4 Spheres Example 1B: Finding Volumes of Spheres 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 Holt McDougal Geometry 11-4 Spheres Example 1C: Finding Volumes of Spheres Find the volume of the hemisphere. Holt McDougal Geometry

11-4 Spheres Check It Out! Example 1 Find the radius of a sphere with volume 2304 ft3. Volume of a sphere Substitute for V. r = 12 ft Holt McDougal Geometry Simplify. 11-4 Spheres Example 3A: Finding Surface Area of Spheres

Find the volume and surface area of a sphere with diameter 76 cm. Give your answers in terms of . S = 4r2 Surface area of a sphere S = 4(38)2 = 5776 cm2 Holt McDougal Geometry 11-4 Spheres Example 3B: Finding Surface Area of Spheres

Find the volume of a sphere with surface area 324 in2. Give your answers in terms of . S = 4r2 324 = 4r2 r=9 Surface area of a sphere Substitute 324 for S. Solve for r. Substitute 9 for r. The volume of the sphere is 972 in2. Holt McDougal Geometry

11-4 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. A = r2 49 = r2 r=7 Area of a circle Substitute 49 for A. Solve for r.

S = 4r2 = 4(7)2 = 196 mi2 Substitute 7 for r. Holt McDougal Geometry 11-4 Spheres Check It Out! Example 3 Find the volume and surface area of the sphere. S = 4r2 S = 4(25)2 Surface area of a sphere

Substitute 25 for r. S = 2500 cm2 Holt McDougal Geometry 11-4 Spheres How to find Volume, Surface Area, and Perimeters of similar solids: If two polyhedra are similar, then their volumes, surface areas, and perimeters have special properties. If the ratio of the similar polyhedra is a, then:

b The ratio of the perimeters is a/b. The ratio of the surface areas is a2/b2. The ratio of the volumes is a3/b3. Ex: Two hexagonal prisms are similar with a ratio of 2/3, what is the ratio of the volumes? The surface areas? Ex: Two pentagonal pyramids are similar with a ratio of , if the smaller pentagonal pyramid has a volume of 12, what is the volume of the larger pentagon?

Ex: Two cubes are similar with side lengths 4cm and 12cm. What are the ratios of the volumes and surface areas? Holt McDougal Geometry

## Recently Viewed Presentations

• Hours Minutes There are 60 minutes in an hour so convert these times in minutes to hours (in decimal notation). Minutes to hours Hours to minutes Write as a fraction compared with 60 minutes (in an hour) Multiply by 60...
• Human Body and . Health Topics Unit. Areas of focus: Form Follows Function concept spread throughout. Levels of biological organization, cell basics, cells of the body, tissues, organs, organ systems, homeostasis, functions of the skeletal system, categories of bones, marrow,...
• GW Italian classification: chemical status Class 1 Null or negligible anthropic impact with valuable hydro chemical characteristics Class 2 Reduced or sustainable anthropic impact over a long period and with good hydro chemical characteristics
• Working with ranges in pictures Barb Ericson Georgia Institute of Technology Feb 2010 03-ConditionalsInPictures
• Vi­her­ryt­tä­mis­tu­kea mak­se­taan maa­ti­lan tuki­kel­poi­sel­le maa­ta­lous­maal­le enin­tään vil­je­li­jän hal­lin­nas­sa ole­via tuki­oi­keuk­sia vas­taa­val­le alal­le.
• Juan has baked a cake and wants to sell it in his bakery. He is going to cut it into 12 slices and sell them individually. He wants to sell it for three times the cost of making it. The...
• Dénommée Tchad Net, son réseau est de classe C. Raccordé au Backbone Internet de France Télécom à Bagnolet et Passtourel en région parisienne, il offre plusieurs services à savoir : - Les courriers électroniques - L'hébergement des sites WEB -...
• Joinery Joinery is the part of Woodworking that involves joining pieces of wood together Some require fasteners, adhesives Types of Wood Joints Butt Joint The simple butt joint is most commonly used. This joint is formed by nailing or screwing...