Elementary Geometry For College Students, 7e
7th Edition
ISBN: 9781337614085
Author: Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher: Cengage,
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Chapter 9.3, Problem 16E
In Exercises 15 to 20, use that fact that
Find the length of the slant height
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HOMEWORK: 18, 19, 24, 27, 29
***Please refer to the HOMEWORK sheet from Thursday, 9/14, for
the problems
****Please text or email me if you have any questions
18. Figure 5-35 is a map of downtown Royalton, showing
the Royalton River running through the downtown
area and the three islands (A, B, and C) connected to
each other and both banks by eight bridges. The Down-
town Athletic Club wants to design the route for a
marathon through the downtown area. Draw a graph
that models the layout of Royalton.
FIGURE 5-35
North Royalton
Royalton River
South Royption
19. A night watchman must walk the streets of the Green
Hills subdivision shown in Fig. 5-36. The night watch-
man needs to walk only once along each block. Draw a
graph that models this situation.
Solve this question and check if my answer provided is correct
Proof: LN⎯⎯⎯⎯⎯LN¯ divides quadrilateral KLMN into two triangles. The sum of the angle measures in each triangle is ˚, so the sum of the angle measures for both triangles is ˚. So, m∠K+m∠L+m∠M+m∠N=m∠K+m∠L+m∠M+m∠N=˚. Because ∠K≅∠M∠K≅∠M and ∠N≅∠L, m∠K=m∠M∠N≅∠L, m∠K=m∠M and m∠N=m∠Lm∠N=m∠L by the definition of congruence. By the Substitution Property of Equality, m∠K+m∠L+m∠K+m∠L=m∠K+m∠L+m∠K+m∠L=°,°, so (m∠K)+ m∠K+ (m∠L)= m∠L= ˚. Dividing each side by gives m∠K+m∠L=m∠K+m∠L= °.°. The consecutive angles are supplementary, so KN⎯⎯⎯⎯⎯⎯∥LM⎯⎯⎯⎯⎯⎯KN¯∥LM¯ by the Converse of the Consecutive Interior Angles Theorem. Likewise, (m∠K)+m∠K+ (m∠N)=m∠N= ˚, or m∠K+m∠N=m∠K+m∠N= ˚. So these consecutive angles are supplementary and KL⎯⎯⎯⎯⎯∥NM⎯⎯⎯⎯⎯⎯KL¯∥NM¯ by the Converse of the Consecutive Interior Angles Theorem. Opposite sides are parallel, so quadrilateral KLMN is a parallelogram.
Chapter 9 Solutions
Elementary Geometry For College Students, 7e
Ch. 9.1 - Consider the solid shown. a Does it appear to be a...Ch. 9.1 - Consider the solid shown. a Does it appear to be a...Ch. 9.1 - Consider the hexagonal prism shown in Exercise 1....Ch. 9.1 - Consider the triangular prism shown in Exercise 2....Ch. 9.1 - Prob. 5ECh. 9.1 - Prob. 6ECh. 9.1 - Suppose that each of the bases of the hexagonal...Ch. 9.1 - Suppose that each of the bases of the triangular...Ch. 9.1 - Suppose that each of bases of the hexagonal prism...Ch. 9.1 - Suppose that each of the bases of the triangular...
Ch. 9.1 - A solid is an octagonal prism. a How many vertices...Ch. 9.1 - A solid is a pentagonal prism. a How many vertices...Ch. 9.1 - Generalize the results found in Exercise 11 and 12...Ch. 9.1 - In the accompanying regular pentagonal prism,...Ch. 9.1 - In the regular pentagonal prism shown above,...Ch. 9.1 - For the right triangular prism, suppose that the...Ch. 9.1 - For the right triangular prism found in Exercise...Ch. 9.1 - Prob. 18ECh. 9.1 - Given that 12 in. =1 ft, find the number of cubic...Ch. 9.1 - Find the volume and the surface area of a closed...Ch. 9.1 - Find the volume and the surface area of a closed...Ch. 9.1 - A cereal box measures 2 in. by 8 in. by 10 in....Ch. 9.1 - The measures of the sides of the square base of a...Ch. 9.1 - For a given box, the height measures 4 m. If the...Ch. 9.1 - For the box shown, the total area is 94 cm2....Ch. 9.1 - If the volume of the box is 252 in3, find the...Ch. 9.1 - The box with dimensions indicated is to be...Ch. 9.1 - A hollow steel door is 32 in. wide by 80 in. tall...Ch. 9.1 - A storage shed is in the shape of a pentagonal...Ch. 9.1 - A storage shed is in the shape of a trapezoidal...Ch. 9.1 - Prob. 31ECh. 9.1 - Prob. 32ECh. 9.1 - When the length of each edge of a cube is...Ch. 9.1 - The numerical value of the volume of a cube equals...Ch. 9.1 - The sum of the lengths of all edges of a cube is...Ch. 9.1 - Prob. 36ECh. 9.1 - Zaidah plans a raised flower bed 2 ft high by 12...Ch. 9.1 - In excavating for a new house, the Philpott...Ch. 9.1 - Kristine creates an open box by cutting congruent...Ch. 9.1 - As in Exercise 39, find the volume of the box if...Ch. 9.1 - For Exercise 41 to 44, 1 ft3 of liquid corresponds...Ch. 9.1 - For Exercise 41 to 44, 1 ft3 of liquid corresponds...Ch. 9.1 - Prob. 43ECh. 9.1 - For Exercise 41 to 44, 1 ft3 of liquid corresponds...Ch. 9.1 - For Exercise 45 to 47, consider the oblique...Ch. 9.1 - For Exercise 45 to 47, consider the oblique...Ch. 9.1 - For Exercise 45 to 47, consider the oblique...Ch. 9.1 - It can be shown that the length of a diagonal of a...Ch. 9.1 - A diagonal of a cube joins two vertices so that...Ch. 9.2 - Prob. 1ECh. 9.2 - Prob. 2ECh. 9.2 - Prob. 3ECh. 9.2 - Prob. 4ECh. 9.2 - Prob. 5ECh. 9.2 - Prob. 6ECh. 9.2 - Prob. 7ECh. 9.2 - Prob. 8ECh. 9.2 - Prob. 9ECh. 9.2 - Prob. 10ECh. 9.2 - Prob. 11ECh. 9.2 - Prob. 12ECh. 9.2 - Prob. 13ECh. 9.2 - Refer to the prisms of Exercises 1 and 2. Which of...Ch. 9.2 - Prob. 15ECh. 9.2 - Refer to the prisms of Exercises 1 and 2. Which of...Ch. 9.2 - Prob. 17ECh. 9.2 - Prob. 18ECh. 9.2 - Prob. 19ECh. 9.2 - Prob. 20ECh. 9.2 - Prob. 21ECh. 9.2 - Prob. 22ECh. 9.2 - Prob. 23ECh. 9.2 - Prob. 24ECh. 9.2 - Prob. 25ECh. 9.2 - Prob. 26ECh. 9.2 - Prob. 27ECh. 9.2 - Prob. 28ECh. 9.2 - Prob. 29ECh. 9.2 - Before the shingles of the steeple see Exercise 29...Ch. 9.2 - Prob. 31ECh. 9.2 - Prob. 32ECh. 9.2 - Prob. 33ECh. 9.2 - Prob. 34ECh. 9.2 - Prob. 35ECh. 9.2 - Prob. 36ECh. 9.2 - Prob. 37ECh. 9.2 - Prob. 38ECh. 9.2 - Prob. 39ECh. 9.2 - Prob. 40ECh. 9.2 - Prob. 41ECh. 9.2 - Prob. 42ECh. 9.2 - Prob. 43ECh. 9.2 - Prob. 44ECh. 9.2 - Prob. 45ECh. 9.3 - Does a right circular cylinder such as an aluminum...Ch. 9.3 - Does a right circular cone such as a wizards cap...Ch. 9.3 - Prob. 3ECh. 9.3 - Prob. 4ECh. 9.3 - For the right circular cylinder, suppose that r=5...Ch. 9.3 - Suppose that r=12 cm and h=15 cm in the right...Ch. 9.3 - The tin can shown at the right has the indicated...Ch. 9.3 - Prob. 8ECh. 9.3 - If the exact volume of a right circular cylinder...Ch. 9.3 - Suppose that the volume of an aluminum can is to...Ch. 9.3 - For an aluminum can, the lateral surface area is...Ch. 9.3 - Find the height of a storage tank in the shape of...Ch. 9.3 - Find the volume of the oblique circular cylinder....Ch. 9.3 - A cylindrical orange juice container has metal...Ch. 9.3 - Prob. 15ECh. 9.3 - In Exercises 15 to 20, use that fact that r2+h2=l2...Ch. 9.3 - Prob. 17ECh. 9.3 - In Exercises 15 to 20, use that fact that r2+h2=l2...Ch. 9.3 - Prob. 19ECh. 9.3 - Prob. 20ECh. 9.3 - The oblique circular cone has an altitude and a...Ch. 9.3 - For the accompanying right circular cone, h=6 m...Ch. 9.3 - Prob. 23ECh. 9.3 - Rukia discovers that the teepee with a circular...Ch. 9.3 - Prob. 25ECh. 9.3 - Prob. 26ECh. 9.3 - Prob. 27ECh. 9.3 - A triangle has sides that measure 15 cm, 20 cm,...Ch. 9.3 - Prob. 29ECh. 9.3 - Prob. 30ECh. 9.3 - If a right circular cone has a circular base with...Ch. 9.3 - A right circular cone has a slant height of 12 ft...Ch. 9.3 - A solid is formed by cutting a conical section...Ch. 9.3 - Prob. 34ECh. 9.3 - In Exercises 34 and 35, give a paragraph proof for...Ch. 9.3 - For a right circular cone, the slant height has a...Ch. 9.3 - For a right circular cone, the ratio of the slant...Ch. 9.3 - If the length of the radius and the height of a...Ch. 9.3 - Prob. 39ECh. 9.3 - For a right circular cone, the dimensions are r=6...Ch. 9.3 - A cylindrical storage tank has a depth of 5 ft and...Ch. 9.3 - If the tank in Exercises 41 needs to be painted...Ch. 9.3 - A frustum of a cone is the portion of the cone...Ch. 9.3 - In Exercises 44 and 45, use the formula from...Ch. 9.3 - In Exercises 44 and 45, use the formula from...Ch. 9.3 - Prob. 46ECh. 9.3 - Richard has a fuel tank in the shape of a right...Ch. 9.3 - When radii OA and OB are placed so that they...Ch. 9.3 - A lawn roller in the shape of a right circular...Ch. 9.4 - Which of these two polyhedrons is concave? Note...Ch. 9.4 - For Figure a of Exercise 1, find the number of...Ch. 9.4 - Prob. 3ECh. 9.4 - For a regular tetrahedron, find the number of...Ch. 9.4 - For a regular hexahedron, find the number of...Ch. 9.4 - A regular polyhedron has 12 edges and 8 vertices....Ch. 9.4 - A regular polyhedron has 12 edges and 6 vertices....Ch. 9.4 - A polyhedron not regular has 10 vertices and 7...Ch. 9.4 - A polyhedron not regular has 14 vertices and 21...Ch. 9.4 - Prob. 10ECh. 9.4 - Prob. 11ECh. 9.4 - Prob. 12ECh. 9.4 - In sphere O, the length of radius OP- is 6 in....Ch. 9.4 - Find the approximate surface area and volume of...Ch. 9.4 - Find the total area surface area of a regular...Ch. 9.4 - Find the total area surface area of a regular...Ch. 9.4 - Find the total area surface area of a regular...Ch. 9.4 - Prob. 18ECh. 9.4 - Prob. 19ECh. 9.4 - Prob. 20ECh. 9.4 - Find the approximate volume of a sphere with...Ch. 9.4 - Prob. 22ECh. 9.4 - The surface of a soccer ball is composed of 12...Ch. 9.4 - A calendar is determined by using each of the 12...Ch. 9.4 - A sphere is inscribed within a right circular...Ch. 9.4 - In calculus, it can be shown that the largest...Ch. 9.4 - Given that a regular polyhedron of n faces is...Ch. 9.4 - A right circular cone is inscribed in a sphere. If...Ch. 9.4 - A sphere is inscribed in a right circular cone...Ch. 9.4 - In Exercises 31 and 32, use the calculator value...Ch. 9.4 - Prob. 32ECh. 9.4 - A sphere has a volume equal to 997in3. Determine...Ch. 9.4 - Prob. 34ECh. 9.4 - The spherical storage tank described in Example 5...Ch. 9.4 - An observatory has the shape of a right circular...Ch. 9.4 - A leather soccer ball has an inside diameter...Ch. 9.4 - An ice cream cone is filled with ice cream as...Ch. 9.4 - For Exercises 39 to 44, make drawings as needed....Ch. 9.4 - For Exercises 39 to 44, make drawings as needed....Ch. 9.4 - For Exercises 39 to 44, make drawings as needed....Ch. 9.4 - For Exercises 39 to 44, make drawings as needed....Ch. 9.4 - For Exercises 39 to 44, make drawings as needed....Ch. 9.4 - For Exercises 39 to 44, make drawings as needed....Ch. 9.4 - Prob. 45ECh. 9.4 - Suppose that a semicircular region with vertical...Ch. 9.4 - Prob. 47ECh. 9.4 - Sketch the solid that results when the given...Ch. 9.4 - Explain how the following formula used in Example...Ch. 9.4 - Prob. 50ECh. 9.CR - Each side of the base of a right octagonal prism...Ch. 9.CR - The base of a right prism is a triangle whose...Ch. 9.CR - The height of a square box is 2 in. more than...Ch. 9.CR - Prob. 4CRCh. 9.CR - The base of a right prism is a triangle whose...Ch. 9.CR - The base of a right prism is a regular hexagon...Ch. 9.CR - Prob. 7CRCh. 9.CR - Prob. 8CRCh. 9.CR - Prob. 9CRCh. 9.CR - The diameter of the base of a right circular cone...Ch. 9.CR - Prob. 11CRCh. 9.CR - Prob. 12CRCh. 9.CR - The radius length of the base of a right circular...Ch. 9.CR - a For the through in the shape of half-cylinder,...Ch. 9.CR - The slant height of a right circular cone is 12...Ch. 9.CR - The volume of the right circular cone is 96 in. If...Ch. 9.CR - Find the surface area of a sphere if the radius...Ch. 9.CR - Find the volume of a sphere if the diameter has...Ch. 9.CR - The solid shown consists of a hemisphere half of a...Ch. 9.CR - If the radius length of one sphere is three times...Ch. 9.CR - Find the volume of the solid of revolution that...Ch. 9.CR - Prob. 22CRCh. 9.CR - Find the exact volume of the solid of revolution...Ch. 9.CR - A plastic pipe is 3 ft long and has an inside...Ch. 9.CR - Prob. 25CRCh. 9.CR - Prob. 26CRCh. 9.CR - A drug manufacturing company wants to manufacture...Ch. 9.CR - Prob. 28CRCh. 9.CR - Find the volume of cement used in the block shows.Ch. 9.CR - Given a die in the shape of a regular octahedron,...Ch. 9.CR - Find the total surface area of a a regular...Ch. 9.CR - Three spheres are externally tangent to each other...Ch. 9.CT - For the regular pentagonal prism shown below, find...Ch. 9.CT - Prob. 2CTCh. 9.CT - Prob. 3CTCh. 9.CT - Prob. 4CTCh. 9.CT - Prob. 5CTCh. 9.CT - Prob. 6CTCh. 9.CT - Prob. 7CTCh. 9.CT - Determine whether the statement is true or false....Ch. 9.CT - Prob. 9CTCh. 9.CT - Prob. 10CTCh. 9.CT - Prob. 11CTCh. 9.CT - Prob. 12CTCh. 9.CT - Prob. 13CTCh. 9.CT - Prob. 14CTCh. 9.CT - Prob. 15CTCh. 9.CT - Prob. 16CT
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