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Section 9-5

Section 9-5. Volume and Surface Area. Volume and Surface Area. Space Figures Volume and Surface Area of Space Figures. Space Figures. Space figures take three dimensions of space to represent the figure.

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Section 9-5

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  1. Section 9-5 • Volume and Surface Area

  2. Volume and Surface Area • Space Figures • Volume and Surface Area of Space Figures

  3. Space Figures Space figures take three dimensions of space to represent the figure. One important group of space figures is a group called polyhedra.The faces of these figures are made only of polygons.

  4. Regular Polyhedra (Platonic Solids) See pictures on the next slide.

  5. Space Figures

  6. Space Figures The next slide shows space includes two other polyhedra: pyramids and prisms. Pyramids are made of triangular sides and a polygonal base. Prisms have two faces in parallel planes; these faces are congruent polygons. The next slide also shows a torus which is a doughnut-shaped solid and figures made up in part of circles including right circular cones and right circular cylinders.

  7. Space Figures

  8. Volume and Surface Area Volume is a measure of capacity of a space figure. Volume is measured in cubic units. Surface Area is the total area that would be covered if the space figure were “peeled” and the peel laid flat. Surface area is measured in square units.

  9. Volume of Surface Area of a Box The volume V and surface area S of a box with length l, width w, and height h is given by the formulas h w l

  10. Example: Volume of Surface Area of a Box Find the volume and surface area of the box below. 3 in. 2 in. 7 in. Solution

  11. Volume of Surface Area of a Cube The volume V and surface area S of a cube with edge of length s is given by the formulas s s s

  12. Example: Volume of Surface Area of a Cube Find the volume and surface area of the cube below. Solution 5 ft.

  13. Volume of Surface Area of a Right Circular Cylinder The volume V and surface area S of a right circular cylinder with base radius r and height h is given by the formulas h r

  14. Example: Volume of Surface Area of a Right Circular Cylinder Find the volume and surface area of the cylinder below. 10 m Solution 2 m

  15. Volume of Surface Area of a Sphere The volume V and surface area S of a sphere radius r is given by the formulas r

  16. Example: Volume of Surface Area of a Sphere Find the volume and surface area of the sphere below. 9 in. Solution

  17. Volume of Surface Area of a Right Circular Cone The volume V and surface area S of a right circular cone with base radius r and height h is given by the formulas h r

  18. Example: Volume of Surface Area of a Right Circular Cone Find the volume and surface area of the cone below. 4 m 3 m Solution

  19. Volume of a Pyramid The volume V of a pyramid with height h and base of area B is given by the formulas h

  20. Example: Volume of a Pyramid Find the volume and surface area of the pyramid (rectangular base) below. 7 cm Solution 3 cm 6 cm

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