P Preliminary Concepts 1 Line And Angle Relationships 2 Parallel Lines 3 Triangles 4 Quadrilaterals 5 Similar Triangles 6 Circles 7 Locus And Concurrence 8 Areas Of Polygons And Circles 9 Surfaces And Solids 10 Analytic Geometry 11 Introduction To Trigonometry A Appendix Chapter9: Surfaces And Solids
9.1 Prisms, Area And Volume 9.2 Pyramids, Area, And Volume 9.3 Cylinders And Cones 9.4 Polyhedrons And Spheres 9.CR Review Exercises 9.CT Test Section9.4: Polyhedrons And Spheres
Problem 1E: Which of these two polyhedrons is concave? Note that the interior dihedral angle formed by the... Problem 2E: For Figure a of Exercise 1, find the number of faces, vertices, and edges in the polyhedron. Then... Problem 3E Problem 4E: For a regular tetrahedron, find the number of faces, vertices, and edges in the polyhedron. Then... Problem 5E: For a regular hexahedron, find the number of faces, vertices, and edges in the polyhedron. Then... Problem 6E: A regular polyhedron has 12 edges and 8 vertices. a Use Eulers equation to find the number of faces.... Problem 7E: A regular polyhedron has 12 edges and 6 vertices. a Use Eulers equation to find the number of faces.... Problem 8E: A polyhedron not regular has 10 vertices and 7 faces. How many edges does it have ? Problem 9E: A polyhedron not regular has 14 vertices and 21 edges. How many faces must it have ? Problem 10E Problem 11E Problem 12E Problem 13E: In sphere O, the length of radius OP- is 6 in. Find the length of the chord: a QR- if QOR=90 b QS-... Problem 14E: Find the approximate surface area and volume of the sphere if OP = 6 in. Use your calculator.... Problem 15E: Find the total area surface area of a regular octahedron if the area of each face is 5.5in2. Problem 16E: Find the total area surface area of a regular dodecahedron 12 faces if the area of each face is... Problem 17E: Find the total area surface area of a regular hexahedron if each edge has a length of 4.2 cm. Problem 18E Problem 19E Problem 20E Problem 21E: Find the approximate volume of a sphere with radius length r= 2.7 cm. Problem 22E Problem 23E: The surface of a soccer ball is composed of 12 regular pentagons and 20 regular hexagons. With each... Problem 24E: A calendar is determined by using each of the 12 faces of a regular dodecahedron for one month of... Problem 25E: A sphere is inscribed within a right circular cylinder whose altitude and diameter have equal... Problem 27E: In calculus, it can be shown that the largest possible volume for the inscribed right circular... Problem 28E: Given that a regular polyhedron of n faces is inscribed in a sphere of radius length 6 in., find the... Problem 29E: A right circular cone is inscribed in a sphere. If the slant height of the cone has a length equal... Problem 30E: A sphere is inscribed in a right circular cone whose slant height has a length equal to that of the... Problem 31E: In Exercises 31 and 32, use the calculator value of . For a sphere whose radius has length 3m, find... Problem 32E Problem 33E: A sphere has a volume equal to 997in3. Determine the length of the radius of the sphere. Use227. Problem 34E Problem 35E: The spherical storage tank described in Example 5 had a length of radius of 3ft. Because the tank... Problem 36E: An observatory has the shape of a right circular cylinder surmounted by a hemisphere. If the radius... Problem 37E: A leather soccer ball has an inside diameter length of 8.5 in. and thickness of 0.1 in. Find the... Problem 38E: An ice cream cone is filled with ice cream as shown. What is the volume of the ice cream? Use your... Problem 39E: For Exercises 39 to 44, make drawings as needed. Can two spheres a be internally tangent? b have no... Problem 40E: For Exercises 39 to 44, make drawings as needed. If two spheres intersect at more than one point,... Problem 41E: For Exercises 39 to 44, make drawings as needed. Two planes are tangent to a sphere at the endpoints... Problem 42E: For Exercises 39 to 44, make drawings as needed. Plane R is tangent to a sphere O at point T. How... Problem 43E: For Exercises 39 to 44, make drawings as needed. Two tangent segments are drawn to sphere Q from... Problem 44E: For Exercises 39 to 44, make drawings as needed. How many common tangent planes do two externally... Problem 45E Problem 46E: Suppose that a semicircular region with vertical diameter of length 4 is rotated about that... Problem 47E Problem 48E: Sketch the solid that results when the given circle of radius length 1 unit is revolved about the... Problem 49E: Explain how the following formula used in Example 6 was obtained: V=43R3-43r3 Problem 50E Problem 48E: Sketch the solid that results when the given circle of radius length 1 unit is revolved about the...
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