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11-1 Space Figures and Cross Sections

11-1 Space Figures and Cross Sections. Polyhedra. A polyhedron is a three- dimensional figure whose surfaces are polygons.

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11-1 Space Figures and Cross Sections

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  1. 11-1 Space Figures and Cross Sections

  2. Polyhedra • A polyhedron is a three- dimensional figure whose surfaces are polygons. • Each polygon is a faceof the polyhedron. • An edgeis a segment that is formed by the intersection of two faces. • A vertex is a point where three or more edges intersect. • A regular polyhedron is one where all the faces are congruent regular polygons.

  3. Identifying Vertices, Edges, and Faces How many vertices, edges, and faces are in each polyhedron?

  4. Cross Sections • A cross section is the intersection of a solid and a plane. What is the cross section formed by the plane and the solid?

  5. 11-2 Surface Areas of Prisms and Cylinders

  6. Prisms • A prism is a polyhedron with two congruent, parallel faces, called bases. • The other faces are lateral faces. • A prism is named by the shape of its bases.

  7. More About Prisms • The altitude, or height, of a prism is the perpendicular distance between the bases. • In a right prism, the lateral faces are rectangles and a lateral edge is an altitude. • In an oblique prism, some or all of the lateral faces are nonrectangular. • Assume prisms are right prisms unless stated or pictured otherwise.

  8. Lateral and Surface Areas • The lateral area (LA) of a prism is the sum of the areas of the lateral faces. • The product of the perimeter of the BASE and the height of the prism LA = Ph • The surface area (SA) is the sum of the lateral area and the area of the two bases (ALL surfaces). SA = LA + 2B

  9. Finding Surface Area of a Prism • What is the surface area of the prism?

  10.  Answer each of the following: • What is the lateral area of the prism? • What is the area of the base? • What is the surface are of the prism?

  11. Cylinders • A cylinder is a solid that has two congruent parallel bases that are circles. • The altitude, or height, is the perpendicular distance between the bases. • In a right cylinder, the segment joining the centers of the bases is the height. • In an oblique cylinder, it is not. • Assume cylinders are right, unless stated or pictured otherwise.

  12. Cylinder Areas • If you were to “unroll” a cylinder, the resulting rectangle is the lateral area. LA = 2πrh • The surface area is the sum of the lateral area and the areas of both bases. SA = LA + 2πr2

  13. Finding Surface Area of a Cylinder • The radius of the base of a cylinder is 4 in. and its height is 6 in. What is the surface area of the cylinder in terms of π.

  14. The radius of the base of a cylinder is 10 cm and its height is 9 cm. What is the surface area of the cylinder in terms of π.

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