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# Geom12point6 97

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### Geom12point6 97

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