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 24E: A calendar is determined by using each of the 12 faces of a regular dodecahedron for one month of...
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Find the surface area and volume for the following prism. Notice that the base is an isosceles triangle .
Transcribed Image Text: This image depicts a three-dimensional geometric shape known as a triangular prism. It includes the following dimensions:
- The triangular face on the side has a height labeled as 5 units.
- The base of the triangular face is labeled as 6 units.
- Another side of the triangular face is marked as 4 units, indicating this is a right triangle because there is a right angle marked between the 4-unit side and 6-unit base.
- The prism has a length of 14 units, which is the length of the rectangle that forms the sides of the prism.
The dashed lines indicate hidden edges within the prism, showing that the shape has depth and is not just a flat surface. The dotted line inside the triangular face represents the height from the right angle to the hypotenuse (5 units).
This diagram is often used in educational contexts to teach students about the properties and volume of prisms.
Polygon with three sides, three angles, and three vertices. Based on the properties of each side, the types of triangles are scalene (triangle with three three different lengths and three different angles), isosceles (angle with two equal sides and two equal angles), and equilateral (three equal sides and three angles of 60°). The types of angles are acute (less than 90°); obtuse (greater than 90°); and right (90°).
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