Mathematics for Machine Technology

John C. Peterson, Robert D. Smith

Chapter 62 Volumes of Prisms and Cylinders - all with Video Answers

Educators

Chapter Questions

Problem 1

Find the volume of a steel shaft that is $18.64 \mathrm{~cm}$ long and has a radius of $1.75 \mathrm{~cm}$. Round your answer to 2 decimal places.

Nishant Kumar

Numerade Educator

01:09

Problem 2

Determine the area of a sector with a radius of $10 \frac{5}{8}$ in. and a central angle of $50^{\circ}$. Round your answer to 2 decimal places.

Dharmendra Jain

Numerade Educator

00:50

Problem 3

Find the area of a triangle with sides that are $4 \frac{1}{8}$ in., $5 \frac{3}{4}$ in., and $6 \frac{1}{2}$ in. long. Round your answer to 2 decimal places.

Ashley High

Numerade Educator

02:24

Problem 4

What is the perimeter of the piece in this figure? Round the answer to 2 decimal places
( FIGURE CAN'T COPY )

Ankit Gupta

Numerade Educator

01:11

Problem 5

Determine the values of $\angle 1$ through $\angle 10$.
( FIGURE CAN'T COPY )

Carson Merrill

Numerade Educator

Problem 6

A $2 \frac{3}{4}$-inch diameter high speed drill running at $68 \mathrm{rpm}$ is used to rough mill a steel casting. What is the cutting speed? Round the answer to the nearest whole number.

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00:26

Problem 7

Express each volume as indicated. Round each answer to the same number of significant digits as in the original quantity.
4320 cubic inches as cubic feet____________

Ashley Volpe

Numerade Educator

00:26

Problem 8

Express each volume as indicated. Round each answer to the same number of significant digits as in the original quantity.
850 cubic inches as cubic feet____________

Ashley Volpe

Numerade Educator

00:26

Problem 9

Express each volume as indicated. Round each answer to the same number of significant digits as in the original quantity.
117 cubic feet as cubic yards____________

Ashley Volpe

Numerade Educator

00:26

Problem 10

Express each volume as indicated. Round each answer to the same number of significant digits as in the original quantity.
182 cubic feet as cubic yards____________

Ashley Volpe

Numerade Educator

Problem 11

Express each volume as indicated. Round each answer to the same number of significant digits as in the original quantity.
12,900 cubic inches as cubic feet ____________

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Problem 12

Express each volume as indicated. Round each answer to the same number of significant digits as in the original quantity.
1.650 cubic feet as cubic inches ____________

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Problem 13

Express each volume as indicated. Round each answer to the same number of significant digits as in the original quantity.
0.325 cubic feet as cubic inches ____________

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00:59

Problem 14

Express each volume as indicated. Round each answer to the same number of significant digits as in the original quantity.
0.1300 cubic yards as cubic inches ____________

Victor Salazar

Numerade Educator

01:18

Equivalent Metric Units of Volume Measure
Express each volume as indicated. Round each answer to the same number of significant digits as in the original quantity.
2700 cubic millimeters as cubic centimeters ____________

Emily Himsel

Numerade Educator

00:12

Problem 16

Equivalent Metric Units of Volume Measure
Express each volume as indicated. Round each answer to the same number of significant digits as in the original quantity.
30.05 cubic millimeters as cubic centimeters ____________

Julie Silva

Numerade Educator

01:18

Problem 17

Equivalent Metric Units of Volume Measure
Express each volume as indicated. Round each answer to the same number of significant digits as in the original quantity.
78 cubic centimeters as cubic millimeters ____________

Emily Himsel

Numerade Educator

01:18

Problem 18

Equivalent Metric Units of Volume Measure
Express each volume as indicated. Round each answer to the same number of significant digits as in the original quantity.
260.1 cubic centimeters as cubic meters ____________

Emily Himsel

Numerade Educator

01:18

Problem 19

Equivalent Metric Units of Volume Measure
Express each volume as indicated. Round each answer to the same number of significant digits as in the original quantity.
0.075 cubic meters as cubic centimeters ____________

Emily Himsel

Numerade Educator

00:12

Problem 20

Equivalent Metric Units of Volume Measure
Express each volume as indicated. Round each answer to the same number of significant digits as in the original quantity.
0.109 cubic centimeters as cubic millimeters ____________

Julie Silva

Numerade Educator

Problem 21

Equivalent Metric Units of Volume Measure
Express each volume as indicated. Round each answer to the same number of significant digits as in the original quantity.
0.7302 cubic meters as cubic millimeters ____________

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01:18

Problem 22

Express each volume as indicated. Round each answer to the same number of significant digits as in the original quantity.
0.00374 cubic meters as cubic millimeters ____________

Emily Himsel

Numerade Educator

Problem 23

Express each volume as indicated. Round each answer to the same number of significant digits as in the original quantity.
2.16 cubic inches as cubic millimeters ____________

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01:05

Problem 24

Express each volume as indicated. Round each answer to the same number of significant digits as in the original quantity.
73.06 cubic feet as cubic meters ____________

Suzanne W.

Numerade Educator

Problem 25

Express each volume as indicated. Round each answer to the same number of significant digits as in the original quantity.
0.348 cubic feet as cubic centimeters ____________

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Problem 26

Express each volume as indicated. Round each answer to the same number of significant digits as in the original quantity.
0.004687 cubic feet as cubic millimeters ____________

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Problem 27

Express each volume as indicated. Round each answer to the same number of significant digits as in the original quantity.
273 cubic centimeters as cubic inches ____________

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Problem 28

Express each volume as indicated. Round each answer to the same number of significant digits as in the original quantity.
372.5 cubic millimeters as cubic inches ____________

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Problem 29

Express each volume as indicated. Round each answer to the same number of significant digits as in the original quantity.
137020 cubic millimeters as cubic inches ____________

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00:26

Problem 30

Express each volume as indicated. Round each answer to the same number of significant digits as in the original quantity.
84300 cubic centimeters as cubic feet ____________

Ashley Volpe

Numerade Educator

01:08

Problem 31

Solve these exercises. Where necessary, round the answers to 2 decimal places unless otherwise specified.
Find the volume of a prism with a base area of 125 square inches and a height of 8 inches.__________

Sarah Vo

Numerade Educator

07:22

Problem 32

Compute the volume of a prism with a height of 26.500 centimeters and a base of 610.00 square centimeters.__________

Bobby Barnes

University of North Texas

01:04

Problem 33

One cubic inch of cast iron weighs 0.26 pound. Find the weight of a block of cast iron with a base area of 48 square inches and a height of 5.3 inches. Round the answer to the nearest pound.__________

Suzanne W.

Numerade Educator

01:32

Problem 34

Find the capacity in gallons of a rectangular electroplating tank with a base area of 38.50 square feet and a height of 4.25 feet. One cubic foot has a capacity of 7.5 gallons. Round the answer to the nearest gallon.__________

Steven Clarke

Numerade Educator

02:08

Problem 35

Find the volume of a prism that is 13.82 centimeters high and has an equilateral triangle base that has 9.08 centimeter sides. Round the answer to the nearest cubic centimeter.__________

Brandon Fox

Numerade Educator

00:53

Problem 36

A length of angle iron is shown.__________
( FIGURE CAN'T COPY )
a. Find the volume of the angle iron. Round the answer to the nearest cubic inch.
b. Find the weight of the angle iron if the material weighs 490 pounds per cubic foot. Round the answer to the nearest pound.
( FIGURE CAN'T COPY )

David Collins

Numerade Educator

Problem 37

A steel forging is shown.
a. Find the number of cubic inches contained in the forging. Round the answer to the nearest cubic inch.
b. Find the weight of the forging. The steel weighs 488.5 pounds per cubic foot. Round the answer to the nearest pound..__________

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03:13

Problem 38

A copper casting is in the shape of a prism with an equilateral triangle base. The length of each base side is 17.80 centimeters, and the casting height is 16.23 centimeters. Copper weighs 8.8 grams per cubic centimeter. Determine the weight of the casting in kilograms. One kilogram equals 1000 grams. Round the answer to 2 decimal places..__________

Jay Patel

Numerade Educator

01:35

Problem 39

Determine the number of cubic centimeters of material needed for the cast plate shown. The casting is 3.20 centimeters thick. Round the answers to the nearest thousandth cubic meter..__________
( FIGURE CAN'T COPY )

Brandon Fox

Numerade Educator

01:41

Problem 40

The steel beam shown weighs 7800 kilograms per cubic meter. Determine the weight of the beam to the nearest kilogram.
( FIGURE CAN'T COPY )

Mitchell Riley

Numerade Educator

00:57

Problem 41

Solve the following exercises. Where necessary, round the answers to 2 decimal places unless otherwise specified.
Find the volume of a right circular cylinder with a base area of 76.00 square inches and a height of 8.600 inches.
.__________

Kayleah Tsai

Numerade Educator

01:03

Problem 42

Compute the volume of a right circular cylinder with a height of 0.40 meter and a base area of 0.30 square meter.
.__________

James Kiss

Numerade Educator

Problem 43

A cylindrical container has a base area of 154.0 square inches and a height of 16.00 inches. Find the capacity of the container in gallons. One gallon contains 231 cubic inches..__________

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01:35

Problem 44

Find the volume of a steel shaft that is 59.00 centimeters long and has a diameter of 3.840 centimeters. Round the answer to 1 decimal place..__________

Brandon Fox

Numerade Educator

00:35

Problem 45

Each cylinder of a 6-cylinder engine has a 3.125-inch diameter and a piston stroke of 4.570 inches. Find the total piston displacement of the engine. Round the answer to 1 decimal place..__________

Amy Jiang

Numerade Educator

Problem 46

A 0.460 -inch-diameter brass rod is $8^{\prime} 5 \frac{7^{\prime \prime}}{32}$ long. Round answers a and b to 1 decimal place.
a. Find the volume of the rod in cubic inches.
b. Compute the total weight of 40 rods. Brass weighs 0.300 pound per cubic inch..__________

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06:16

Problem 47

A bronze bushing is shown..__________
( FIGURE CAN'T COPY )
a. Compute the volume of bronze in the bushing.
b. The bushing weighs 1.50 pounds. Find the weight of 1.00 cubic inch of bronze.

Henry York

Numerade Educator

03:30

Problem 48

Find the number of cubic centimeters of material contained in the support base plate shown. The plate is 4.73 centimeters thick..__________
( FIGURE CAN'T COPY )

Jay Patel

Numerade Educator

06:16

Problem 49

The brass used to make the bushing shown weighs 546.2 pounds per cubic foot. All
dimensions are in inches. Find the weight of 2600 bushings. Round the answer to the
nearest pound.__________
( FIGURE CAN'T COPY )

Henry York

Numerade Educator

01:12

Problem 50

Determine the number of cubic millimeters of material contained in the flanged collar
shown. Round the answer to the nearest cubic millimeter. __________
( FIGURE CAN'T COPY )

David Collins

Numerade Educator

02:06

Problem 51

Solve the following exercises. Where necessary, round the answers to 2 decimal places unless otherwise specified.
Find the height of a prism that has a base area of 67.84 square inches and a volume of 512.70 cubic inches.__________

John Mcalister

Numerade Educator

01:14

Problem 52

A solid right circular cylinder is 18.25 centimeters high and contains 119.62 cubic centimeters of material. Compute the cross-sectional area of the cylinder.__________

James Kiss

Numerade Educator

03:49

Problem 53

A solid steel bar 27.60 inches long has a square base. The bar has a volume of 104.00 cubic inches. Compute the length of a side of the base.__________

Sheryl Ezze

Numerade Educator

03:07

Problem 54

A cylindrical quart can has a 3.86-inch diameter. What is the height of the can? (Note: 1 gallon $=231$ cubic inches; 1 gallon $=4$ quarts.)__________

Bobby Barnes

University of North Texas

05:10

Problem 55

A cylinder container 26.20 centimeters high is designed to have a capacity of 1.76 liters. Determine the base area of the container. One liter contains 1000 cubic centimeters.__________

Willis James

Numerade Educator

02:07

Problem 56

A triangular brass casting is shown. The block weighs 15.30 pounds. Brass weighs 526.7 pounds per cubic foot. Compute the height of the block. All dimensions are in inches.__________
( FIGURE CAN'T COPY )

Manisha Sarker

Numerade Educator

Problem 57

A rectangular aluminum plate required for a job is 4 feet 0 inches wide and 5 feet
0 inches long. The maximum allowable weight is 505.5 pounds. Aluminum weighs
168.5 pounds per cubic foot. What is the maximum thickness of the plate? Round the
answer to the nearest tenth inch. __________

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03:27

Problem 58

Determine the cross-sectional area of a regular octagon cross-section tool steel piece
shown. The piece weighs 3.72 pounds. The tool steel weighs 0.284 pound per cubic inch. __________
( FIGURE CAN'T COPY )

Debasish Das

Numerade Educator

02:07

Problem 59

A circular cross-sectional piece of brass rod weighs 8.67 pounds. The piece is cut from a brass rod that weighs 3.66 pounds per foot of length. The piece has a volume of 56.67 cubic inches. Find the area of circular base.__________

Manisha Sarker

Numerade Educator

05:51

Problem 60

Find the length of a piece of bar stock with a regular hexagon cross section with 0.875 -inch sides. The piece has a volume of 31.2 cubic inches. The formula $A \approx 2.598 s^2$ is used to determine the area of a regular hexagon where $A$ is the area and $s$ is the length of a side.__________

Sheryl Ezze

Numerade Educator

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