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
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