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

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Presentation transcript:

11-1 Space Figures and Cross Sections

Polyhedra A polyhedron is a three- dimensional figure whose surfaces are polygons. Each polygon is a face of the polyhedron. An edge is 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.

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

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?

11-2 Surface Areas of Prisms and Cylinders

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.

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.

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

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

 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?

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.

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 + 2πr 2

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.

 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.