Geom12point6 97
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Geom12point6 97 Geom12point6 97 Presentation Transcript

  • Chapter 12 - Surface Area & Volume of Solids
    • Objectives:
    • Identify types of solids
    • Calculate surface area & volume of:
    • Prisms
    • Pyramids
    • Cylinders
    • Cones
    • Spheres
  • 12.6 Surface Area & Volume of Spheres Objectives: Find the volume of a sphere Find the surface area of a sphere
  • What is a sphere?
    • A sphere is the locus of points in space that are a given distance from a point.
    • That point is called the center of the sphere.
    • A radius of a sphere is a segment from the center to a point on the sphere.
    • A chord of a sphere is a segment whose endpoints are on the sphere.
    • A diameter is a chord that contains the center.
  • Surface Area of a Sphere
    • S = 4πr 2
  • More Sphere Terms
    • If a plane intersects a sphere, the intersection is . . .
    • either a single point or a plane
    • 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 the sphere into 2 congruent halves called hemispheres .
  • Example
    • A baseball has a radius of 1.45 inches.
    • How much leather does it take to cover the baseball?
    • S = 4πr 2
    • S = 4π*1.45*1.45
    • S = 26.4 “ 2
  • Volume of a Sphere
    • V = 4/3 πr 3
  • Example
    • To make a steel ball bearing, a cylindrical slug is heated and pressed into a spherical shape with the same volume.
    • Find the radius of the ball bearing.
    h = 2 cm r = 1 cm
  • Example
    • Find the volume of the cylinder:
    • V = πr 2 h = π*1*1*2 = 2π
    • Find the radius of the sphere:
    • V = 4/3 πr 3
    • 2π = 4/3 πr 3 (multiply both sides by 3)
    • 6π = 4πr 3 (Divide each side by 4π)
    • 1.5 = r 3 (take cube root with a calculator)
    • r = 1.14
    h = 2 cm r = 1 cm
  • Do Worksheets
    • Study for tomorrow’s test!