Spheres Course 3 Learn to find the volume and surface area of spheres.
Spheres Course 3 Insert Lesson Title Here Vocabulary sphere hemisphere great circle
Spheres Course 3 A sphere is the set of points in three dimensions that are a fixed distance from a given point, the center. A plane that intersects a sphere through its center divides the two halves or hemispheres. The edge of a hemisphereis agreat circle.
Theorem 12.11: Surface Area of a Sphere • The surface area of a sphere with radius r is S = 4r2.
Ex. 1: Finding the Surface Area of a Sphere • Find the surface area. When the radius doubles, does the surface area double?
S = 4r2 = 422 = 16 in.2 S = 4r2 = 442 = 64 in.2 The surface area of the sphere in part (b) is four times greater than the surface area of the sphere in part (a) because 16 • 4 = 64 So, when the radius of a sphere doubles, the surface area DOES NOT double.
More . . . • If a plane intersects a sphere, the intersection is either a single point or a circle. If the plane contains the center of the sphere, then the intersection is a great circle of the sphere. Every great circle of a sphere separates a sphere into two congruent halves called hemispheres.
Ex. 2: Using a Great Circle • The circumference of a great circle of a sphere is 13.8 feet. What is the surface area of the sphere?
Solution: Begin by finding the radius of the sphere. C = 2r 13.8 = 2r 13.8 2r 6.9 = r = r
Solution: Using a radius of 6.9 feet, the surface area is: S = 4r2 = 4(6.9)2 = 190.44 ft.2 So, the surface area of the sphere is 190.44 ft²
Theorem 12.12: Volume of a Sphere • The volume of a sphere with radius r is • V = 4r3. 3
Spheres 4 3 V = pr3 = p(9)3 4 3 Course 3 Additional Example 1: Finding the Volume of a Sphere Find the volume of a sphere with radius 9 cm, both in terms of p and to the nearest tenth of a unit. Volume of a sphere Substitute 9 for r. = 972p cm3 3,052.1 cm3
Spheres 4 3 V = pr3 Course 3 Try This: Example 1 Find the radius of a sphere given volume of a sphere is 113.1 m³. Find the circumference of the great circle given volume = 72pin³ Volume of a sphere
Spheres Course 3 Insert Lesson Title Here Lesson Quiz: Part 1 Find the volume of each sphere, both in terms of and to the nearest tenth. Use 3.14 for p. 1.r = 4 ft 2.d = 6 m Find the surface area of each sphere, both in terms of and to the nearest tenth. Use 3.14 for p. 85.3p ft3, 267.8 ft3 36p m3, 113.0 m3 1936p in2, 6079.0 in2 3.r = 22 in 4.d = 1.5 mi 2.25p mi2, 7.1 mi2
Spheres Course 3 Insert Lesson Title Here Lesson Quiz: Part 2 5.A basketball has a circumference of 29 in. To the nearest cubic inch, what is its volume? 412 in3