Math

GeometryElementary Geometry for College StudentsIn Exercises 44 and 45, use the formula from Exercise 43. Similar triangles were used to find h and H. A container of yogurt has the shape of a frustum of a cone. With the lower base having diameter length 6 cm and the upper base having diameter length 8 cm, the volume of such a container 7.5 cm tall can be determined by using H = 30 cm and h = 22.5 cm. Find its volume. A frustum of a cone is the portion of the cone bounded between the circular base and a plane parallel to the base. With dimensions are indicated, show that the volume of the frustum of the cone is V = 1 3 π R 2 H − 1 3 π r h 2BuyFind*arrow_forward*

6th Edition

Daniel C. Alexander + 1 other

Publisher: Cengage Learning

ISBN: 9781285195698

Chapter 9.3, Problem 45E

Textbook Problem

*In Exercises 44 and 45, use the formula from Exercise 43. Similar triangles were used to find h and H.*

A container of yogurt has the shape of a frustum of a cone. With the lower base having diameter length

A frustum of a cone is the portion of the cone bounded between the circular base and a plane parallel to the base. With dimensions are indicated, show that the volume of the frustum of the cone is

Elementary Geometry for College Students

Show all chapter solutions

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 - If each edge of the hexagonal prism in Exercise 1...Ch. 9.1 - If each edge of the triangular prism in Exercise...Ch. 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 - Given that 100 cm =1 m, find the number of cubic...Ch. 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 - A cube is a right square prism in which all edges...Ch. 9.1 - Use the formulas and drawing in Exercise 31 to...Ch. 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 - A concrete pad 4 in. thick is to have a length of...Ch. 9.1 - Zaidah plans a raised flower bed 2 ft high by 12...Ch. 9.1 - In excavating for a new house, a contractor digs a...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 - Kiannas aquarium is box-shaped with dimensions of...Ch. 9.1 - The gasoline tank on an automobile is box-shaped...Ch. 9.1 - For Exercise 43 to 45, consider the oblique...Ch. 9.1 - For Exercise 43 to 45, consider the oblique...Ch. 9.1 - For Exercise 43 to 45, 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 - In Exercises 1 to 4, name the solid that is shown....Ch. 9.2 - In Exercises 1 to 4, name the solid that is shown....Ch. 9.2 - In Exercises 1 to 4, name the solid that is shown....Ch. 9.2 - In Exercises 1 to 4, name the solid that is shown....Ch. 9.2 - In the solid shown, base ABCD is a square. a Is...Ch. 9.2 - In the solid on page 406, the base is a regular...Ch. 9.2 - Consider the square pyramid in Exercise 5. a How...Ch. 9.2 - Consider the hexagonal pyramid in Exercise 6. a...Ch. 9.2 - Suppose that the lateral faces of the pyramid in...Ch. 9.2 - Suppose that the base of the hexagonal pyramid in...Ch. 9.2 - Suppose that the base of the square pyramid in...Ch. 9.2 - Suppose that the base of the hexagonal pyramid in...Ch. 9.2 - Assume that the number of sides in the base of a...Ch. 9.2 - Refer to the prisms of Exercises 1 and 2. Which of...Ch. 9.2 - Refer to the pyramids of Exercises 3 and 4. Which...Ch. 9.2 - Refer to the prisms of Exercises 1 and 2. Which of...Ch. 9.2 - Refer to the pyramids of Exercises 3 and 4. Which...Ch. 9.2 - Consider any regular pyramid. Indicate which line...Ch. 9.2 - Consider any regular pyramid. Indicate which line...Ch. 9.2 - In Exercises 20 and 21, use Theorem 9.2.1 in which...Ch. 9.2 - In Exercises 20 and 21, use Theorem 9.2.1 in which...Ch. 9.2 - In a regular pentagonal pyramid, each lateral edge...Ch. 9.2 - In a regular pentagonal pyramid, each base edge...Ch. 9.2 - For the regular square pyramid shown, suppose that...Ch. 9.2 - For the regular square pyramid shown in Exercise...Ch. 9.2 - The figure below is a regular hexagonal pyramid. a...Ch. 9.2 - For a regular square pyramid, suppose that the...Ch. 9.2 - For a regular square pyramid, the slant height of...Ch. 9.2 - A church steeple in the shape of a regular square...Ch. 9.2 - Before the shingles of the steeple see Exercise 29...Ch. 9.2 - A teepee is constructed by using 12 poles. The...Ch. 9.2 - For its occupants to be protected from the...Ch. 9.2 - The street departments storage building, which is...Ch. 9.2 - The foyer planned as an addition to an existing...Ch. 9.2 - The exhaust chute on a wood chipper has a shape...Ch. 9.2 - A popcorn container at a movie theatre has the...Ch. 9.2 - A regular tetrahedron is a regular triangular...Ch. 9.2 - Each edge of a regular tetrahedron see Exercise 37...Ch. 9.2 - Exercise 39 and 40 are based upon the uniqueness...Ch. 9.2 - Exercise 39 and 40 are based upon the uniqueness...Ch. 9.2 - Consider the accompanying figure. When the four...Ch. 9.2 - Find the volume of the regular square pyramid that...Ch. 9.2 - Where e1 and e2 are the lengths of two...Ch. 9.2 - Use the information from Exercise 43 to find the...Ch. 9.2 - A hexagonal pyramid not regular with base ABCDEF...Ch. 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 - For the right circular cylinder shown on page 471,...Ch. 9.3 - For the right circular cylinder shown on page 417,...Ch. 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 - What is the volume of the tin can? If it contains...Ch. 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 - In Exercises 15 to 20, use that fact that r2+h2=l2...Ch. 9.3 - In Exercises 15 to 20, use that fact that r2+h2=l2...Ch. 9.3 - In Exercises 15 to 20, use that fact that r2+h2=l2...Ch. 9.3 - In Exercises 15 to 20, use that fact that r2+h2=l2...Ch. 9.3 - In Exercises 15 to 20, use that fact that r2+h2=l2...Ch. 9.3 - In Exercises 15 to 20, use that fact that r2+h2=l2...Ch. 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 - For the right circular cone shown in Exercise 22,...Ch. 9.3 - Rukia discovers that the teepee with a circular...Ch. 9.3 - A rectangle has dimensions of 6 in. by 3 in. Find...Ch. 9.3 - A rectangle has dimensions of 6in. by 3 in. Find...Ch. 9.3 - A triangle has sides that measure 15 cm, 20 cm,...Ch. 9.3 - A triangle has sides that measure 15 cm, 20 cm,...Ch. 9.3 - A triangle has sides that measure 15 cm, 20 cm,...Ch. 9.3 - Where r is the length of the radius of a sphere,...Ch. 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 - In Exercises 34 and 35, give a paragraph proof for...Ch. 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 - For the two similar cylinders in Exercise 38, what...Ch. 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 - An oil refinery has storage tanks in the shape of...Ch. 9.3 - A farmer 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 - For figure b of Exercise 1, find the number of...Ch. 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 - In Exercises 10 to 12, the probability is the...Ch. 9.4 - In Exercises 10 to 12, the probability is the...Ch. 9.4 - In Exercises 10 to 12, the probability is the...Ch. 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 - Find the total area surface area of a regular...Ch. 9.4 - The total area surface area of a regular...Ch. 9.4 - The total area surface area of a regular...Ch. 9.4 - Find the approximate volume of a sphere with...Ch. 9.4 - Find the approximate volume of a sphere with...Ch. 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 - In Exercises 31 and 32, use the calculator value...Ch. 9.4 - A sphere has a volume equal to 997in3. Determine...Ch. 9.4 - A sphere has a surface area equal to 154in2....Ch. 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 - Suppose that a semicircular region with a vertical...Ch. 9.4 - Suppose that a semicircular region with vertical...Ch. 9.4 - Sketch the torus that results when the given...Ch. 9.4 - Sketch the solid that results when the given...Ch. 9.4 - Explain how the following formula used in Example...Ch. 9.4 - Derive a formula for the total surface area of the...Ch. 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 - The base of a right prism is a rectangle whose...Ch. 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 - A regular square pyramid has a base whose sides...Ch. 9.CR - A regular hexagonal pyramid has a base whose sides...Ch. 9.CR - The radius of the base of a right circular cone...Ch. 9.CR - The diameter of the base of a right circular cone...Ch. 9.CR - The slant height of a regular square pyramid...Ch. 9.CR - The base of a regular pyramid is an equilateral...Ch. 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 - Find the exact volume of the solid of revolution...Ch. 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 - A sphere with a diameter length of 14 in. is...Ch. 9.CR - a An octahedron has _________________ faces that...Ch. 9.CR - A drug manufacturing company wants to manufacture...Ch. 9.CR - For each of the following solids, verify Eulers...Ch. 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 - For the regular pentagonal base, each edge...Ch. 9.CT - For the regular square pyramid shown, find the...Ch. 9.CT - For the regular square pyramid shown above, find a...Ch. 9.CT - For the regular square pyramid shown, find the...Ch. 9.CT - Find the height of the regular square pyramid...Ch. 9.CT - Find the volume of the regular square pyramid...Ch. 9.CT - Determine whether the statement is true or false....Ch. 9.CT - Determine whether the statement is true or false....Ch. 9.CT - Recall Eulers equations, V+F=E+2. For a certain...Ch. 9.CT - Find the slant height of the right circular cone...Ch. 9.CT - For the right circular cylinder shown, r=4 cm and...Ch. 9.CT - The exact volume of a right circular cone not...Ch. 9.CT - Assume that a die used for gaming is in the shape...Ch. 9.CT - A spherical storage tank filled with water has a...Ch. 9.CT - A pump moves water at a rate of 8ft3 per minute....

Find more solutions based on key concepts

Show solutions , Rochester, New York, averages µ = 2 l .9 inches of snow for the month of December. The distribution of snowfa...

Statistics for The Behavioral Sciences (MindTap Course List)

Simplify the algebraic expressions in Problems 1-14 by com- bining similar terms. Objective 1 5a26a2

Intermediate Algebra

Find the radius of convergence and interval of convergence of the series. n=1xn2n1

Calculus (MindTap Course List)

Convert each expression in Exercises 25-50 into its technology formula equivalent as in the table in the text. ...

Applied Calculus

Find the tangential and normal components of the acceleration vector. 38. r(t)=2t2i+(23t32t)j

Multivariable Calculus

In problems 31-38, write the equation of each line described.
34. Through and

Mathematical Applications for the Management, Life, and Social Sciences

Verifying the Divergence Theorem In Exercises 3-8, verify the Divergence Theorem by evaluating SFNdS as a surfa...

Calculus: Early Transcendental Functions

93/4

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

Wire electrical-discharge machining (WEDM) is a process used to manufacture conductive hard metal components. I...

Probability and Statistics for Engineering and the Sciences

Determine whether the argument is an example of inductive reasoning or deductive reasoning. We had rain each da...

Mathematical Excursions (MindTap Course List)

Convert the expressions in Exercises 6584 to power form. 2x3x0.12+43x1.1

Finite Mathematics and Applied Calculus (MindTap Course List)

Exercises You can use the following problems as a self-test on the material presented in this review. If you ca...

Essentials Of Statistics

Checkpoint 9 Worked-out solution available at LarsonAppliedCalculus.com Find the slope of the graph of f(x)=x25...

Calculus: An Applied Approach (MindTap Course List)

In Exercises 3148, (a) factor the given expression, and (b) set the expression equal to zero and solve for the ...

Finite Mathematics

Basic Computation: p Distribution Suppose we have a binomial experiment in which success is defined to be a par...

Understanding Basic Statistics

Use Equation 6 to find dy/dx. 28. cos(xy) = 1 + sin y

Calculus: Early Transcendentals

Describe the homogeneity of variance assumption and explain why it is important for the independent-measures t ...

Essentials of Statistics for The Behavioral Sciences (MindTap Course List)

Systems of Inequalities Graph the solution set of the system of inequalities. Find the coordinates of all verti...

Precalculus: Mathematics for Calculus (Standalone Book)

Find the local and absolute extreme values of the function on the given interval. f(x) = x3 9x2 + 24x 2, [0, ...

Single Variable Calculus: Early Transcendentals, Volume I

A standard bale of cotton weighs approximately 500 lb. How many bales are contained in 15 tons of cotton?

Elementary Technical Mathematics

Find the domain of the function. 31. f(x)=x+4x29

Single Variable Calculus

32. Let be a fixed element of the group . According to Exercise 20 of section 3.5, the mapping defined by is...

Elements Of Modern Algebra

Change of Variables In Exercises 53-60, find the indefinite integral by making a change of variables. x3x4dx

Calculus of a Single Variable

The following problems review material covered in Section 3.5. Arc Length A point is moving with an angular vel...

Trigonometry (MindTap Course List)

Sketch the graph of an example of a function f that satisfies all of the given conditions. limxf(x)=3,limx2f(x)...

Single Variable Calculus: Early Transcendentals

Justin Schaefer owns a home that was recently appraised for $92,900. The balance on his existing first mortgage...

Contemporary Mathematics for Business & Consumers

Solve the linear programming problems. Maximize Subject to P=2x+3y+4z+2wx+2y+3z+2w63x+4y+zy43x+2y2z+3w12x0,y0,z...

Finite Mathematics for the Managerial, Life, and Social Sciences

Continuity on a Closed Interval In Exercises 37-40, discuss the continuity of the function on the closed interv...

Calculus: Early Transcendental Functions (MindTap Course List)

Critical Thinking Determine if the statement is true or false. If the statement is false, then correct it and m...

College Algebra (MindTap Course List)

The best approximation of y using differentials for y = x2 4x at x = 6 when x = dx = 0.03 is: a) 0.36 b) 0.24 ...

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

True or False:
is a convergent series.

Study Guide for Stewart's Multivariable Calculus, 8th

Find each percentage, percent (rate), or base. Round the answers to 2 decimal places when necessary. 72. ? is 4...

Mathematics For Machine Technology

Describe the three techniques used to quantify behavioral observations and the three techniques used for sampli...

Research Methods for the Behavioral Sciences (MindTap Course List)

Find the following F distribution values from Table 4 of Appendix B. a. F.05 with degrees of freedom 5 and 10 b...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

The data from exercise 3 follow. xi 2 6 9 13 20 yi 7 18 9 26 23 a. What is the value of the standard error of t...

Statistics for Business & Economics, Revised (MindTap Course List)

Define the concept of internal validity and a threat to internal validity.

Research Methods for the Behavioral Sciences (MindTap Course List)

Epidemic Model A single infected individual enters a community of n susceptible individuals. Let x be the numbe...

Calculus (MindTap Course List)

In Exercises 25-30, use the information in Figure 9.84. The distances given are not along roads. Rather, they a...

Mathematics: A Practical Odyssey

EXPLORING CONCEPTS Limits If lim(x,y)(2,3)f(x,y)=4, can you conclude anything about f(2, 3)? Explain.

Multivariable Calculus

Fruit Juice May Be Fueling Pudgy Preschoolers, Study Says is the title of an article that appeared in the San L...

Introduction To Statistics And Data Analysis

Weekly Demand at Whole Foods Market. The manager at a Whole Foods Market is responsible for managing store inve...

Essentials Of Statistics For Business & Economics

Using Logistic Regression Exercises S29 through S33 require a calculator that can perform logistic regression. ...

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

38. Refer to exercise 21, where data on the production volume x and total cost y for a particular manufacturing...

Modern Business Statistics with Microsoft Office Excel (with XLSTAT Education Edition Printed Access Card) (MindTap Course List)

A coin is tossed ten times. In each case the outcome H (for heads) or T (for tails) is recorded. (One possible ...

Discrete Mathematics With Applications

[T] A company purchases some computer equipment for $20,500. At the end of a 3-year period, the value of the eq...

Calculus Volume 1

In Problems 1332 use variation of parameters to solve the given nonhomogeneous system. 13. dxdt=3x3y+4dydt=2x2y...

A First Course in Differential Equations with Modeling Applications (MindTap Course List)

For the following exercises, identify (he type of data that would be used to describe a response (quantitative ...

Introductory Statistics