11-1 space figures and cross sections. polyhedra a polyhedron is a three- dimensional figure whose...
TRANSCRIPT
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11-1 Space Figures and Cross Sections
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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.
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Identifying Vertices, Edges, and Faces
How many vertices, edges, and faces are in each polyhedron?
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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?
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11-2 Surface Areas of Prisms and Cylinders
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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.
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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.
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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 prismLA = Ph
• The surface area (SA) is the sum of the lateral area and the area of the two bases (ALL surfaces).
SA = LA + 2B
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Finding Surface Area of a Prism
• What is the surface area of the prism?
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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?
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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.
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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
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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.
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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.