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# Geom12point4and5 97

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### Geom12point4and5 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. 12.4 & 5 Volume of Prisms & Cylinders & Pyramids & Cones Objectives: Find Volume of prisms cylinders pyramids cones
3. 3. What is volume? <ul><li>The volume of a solid is the number of cubic units contained in its interior. </li></ul><ul><li>Volume is measured in cubic units, such as cubic meters (m 3 ) </li></ul>
4. 4. Volume Postulates <ul><li>Volume of a Cube </li></ul><ul><ul><li>The volume of a cube is the cube of the length of its side, or V = s 3 </li></ul></ul><ul><li>Volume Congruence </li></ul><ul><ul><li>If 2 polyhedra are congruent, they have the same volume </li></ul></ul><ul><li>Volume Addition Postulate </li></ul><ul><ul><li>The volume of a solid is the sum of the volumes of all its nonoverlapping parts. </li></ul></ul>
5. 5. Example <ul><li>If a box is 5 inches long, 3 inches wide, and 4 inches, high, what is the volume? </li></ul><ul><li>5*3*4 inches cubed </li></ul><ul><li>60 “ 3 </li></ul>
6. 6. Cavalieri’s Principle <ul><li>If 2 solids have the same height and the same cross-sectional area at every level, then they have the same volume. </li></ul><ul><li>Look at the picture on p. 744 </li></ul>
7. 7. Volume of a Prism <ul><li>The volume V of a prism is V = Bh, </li></ul><ul><ul><li>where B is the area of a base, </li></ul></ul><ul><ul><li>and h is the height. </li></ul></ul>
8. 8. Volume of a Cylinder <ul><li>The volume V of a cylinder is V = Bh =πr 2 h </li></ul><ul><ul><li>where B is the area of a base, </li></ul></ul><ul><ul><li>h is the height, </li></ul></ul><ul><ul><li>And r is the radius of the base. </li></ul></ul>
9. 9. Do example 2, p. 744
10. 10. Volume of a Pyramid <ul><li>The volume V of a pyramid is V = 1/3 Bh </li></ul><ul><ul><li>where B is the area of a base, </li></ul></ul><ul><ul><li>And h is the height </li></ul></ul>
11. 11. Volume of a Cone <ul><li>The volume V of a cone is V = 1/3 Bh = 1/3 πr 2 h </li></ul><ul><ul><li>where B is the area of a base, </li></ul></ul><ul><ul><li>h is the height, </li></ul></ul><ul><ul><li>And r is the radius of the base. </li></ul></ul>
12. 12. Do Example 1, p. 752 <ul><li>And example 2, p. 753 </li></ul><ul><li>Then do worksheets </li></ul>