Mathematics for Machine Technology

John C. Peterson, Robert D. Smith

Chapter 63 Volumes of Pyramids and Cones - all with Video Answers

Educators

Chapter Questions

Problem 1

A rectangular strip of steel $2 \mathrm{ft} 4 \mathrm{in}$. long, $1 \mathrm{ft} 6 \mathrm{in}$. wide, and $\frac{5}{8}$ in. thick has four holes drilled through the strip, each with a diameter of $1 \frac{1}{2}$ in. If steel weighs $0.264 \mathrm{lb} /$ cubic inch, what is the weight of this strip? Round the answer to the nearest pound.

Naman Kumar

Numerade Educator

01:20

Problem 2

In order to make a conical duct, a circular sheet of metal is to be cut in the shape of a sector of a circle. If the radius of the sector is $28.5 \mathrm{in}$. and the arc length of the of the sector is 26.4 in., what are the central angle, $\theta$, and area of the sector?

Carson Merrill

Numerade Educator

01:40

Problem 3

A square bar $\frac{7}{8}$ in. on a side is to be milled from a circular rod. If the available rods are 1 in., $1 \frac{1}{4}$ in., $1 \frac{1}{2}$ in., and 2 in. in diameter, which rod should be used so there is the least waste? How much waste, in area, will there be with the selected rod? Round your answer to 2 decimal places.

Angela Guo

Numerade Educator

00:43

Problem 4

Construct a regular hexagon $3 \mathrm{~cm}$ on a side. By measurement, find the distance across flats to the nearest tenth.

Jay Patel

Numerade Educator

01:02

Problem 5

Two angles of a triangle measure $73^{\circ} 18^{\prime}$ and $49^{\circ} 47^{\prime}$. What is the size of the third angle? Identify the triangle as scalene, isosceles, equilateral, or right.

Mohamed Mohamed

Numerade Educator

Problem 6

Determine the circular pitch of a gear with a whole depth dimension of 0.465 in. Round the answer to 4 decimal places.

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02:44

Problem 7

Compute the volume of a regular pyramid with a base area of 236.90 square inches and a height of 12.84 inches.

Ashley High

Numerade Educator

02:01

Problem 8

Find the volume of a right circular cone with a base area of 38.60 square centimeters and a height of 5.000 centimeters.

Erin Kirchmeier

Numerade Educator

04:09

Problem 9

Find the volume of a regular pyramid with a height of 10.80 inches and a base area of 98.00 square inches.

Dawn Getman

Numerade Educator

02:48

Problem 10

A container is in the shape of a right circular cone. The base area is 63.60 square inches and the height is 7.65 inches. Compute the capacity of the container in gallons. One gallon contains 231 cubic inches.

James Kiss

Numerade Educator

01:56

Problem 11

A brass casting is in the shape of a right circular cone with a base diameter of 8.26 centimeters and a height of 18.36 centimeters. Find the volume. Round the answer to the nearest cubic centimeter.

Erin Kirchmeier

Numerade Educator

00:39

Problem 12

Two solid pieces of aluminum in the shape of right circular cones with different base diameters are machined. The heights of both pieces are 6 inches. The base of the smaller piece is 2 inches in diameter. The base of the larger piece is twice as large, or 4 inches in diameter. How many times heavier is the larger piece than the smaller?

Ashley Volpe

Numerade Educator

03:01

Problem 13

A vessel is in the shape of a right circular cone. This vessel contains liquid to a depth of 12.8 centimeters, as shown. How many liters of liquid must be added in order to fill the vessel? One liter contains 1000 cubic centimeters.

Erika Bustos

Numerade Educator

02:07

Problem 14

A solid iron casting is in the shape of a regular pyramid with a triangular base. Each of the three base sides is 5.70 inches long and the casting is 4.65 inches high. The casting weighs 5.82 pounds.
a. Determine the volume of material in the casting.
b. What is the weight of one cubic inch of cast iron?

Manisha Sarker

Numerade Educator

Problem 15

The No. 3 taper standard lathe center shown has a tungsten-carbide tip with the dimensions given. How many cubic inches of carbide are there in the exposed part of the tip?

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02:30

Problem 16

A piece in the shape of a pyramid with a regular octagon (eight sided) base is machined from a solid block of bronze. Each side of the octagon base is 9.36 inches long. The height of the piece is 7.08 inches. The octagon base area $\approx 4.828 \mathrm{~s}^2$, where $s$ is the length of a side of the octagon.
a. Determine the volume of the piece. Round the answer to the nearest cubic inch.
b. Determine the weight of the piece. Round the answer to the nearest pound.

Barsha Rana

Numerade Educator

00:38

Problem 17

Compute the height of a regular pyramid with a base area of 32.87 square inches and a volume of 152.08 cubic inches.

Amrita Bhasin

Numerade Educator

02:01

Problem 18

A right circular cone 12.7 centimeters high contains 198.7 cubic centimeters of material. Find the area of the base of the cone. Round the answer to the nearest square centimeter.

Erin Kirchmeier

Numerade Educator

02:07

Problem 19

The base area of a thin-walled casting in the shape of a regular pyramid is 49 square inches. The casting contains 323 cubic inches of air space. How high is the casting? Round the answer to the nearest inch.

Hannah Wilds

Numerade Educator

01:32

Problem 20

A container with a capacity of 6.00 gallons is in the shape of a right circular cone. The container is 17.80 inches high. Find the base area of the container. One gallon contains 231 cubic inches.

Ankit Gupta

Numerade Educator

00:32

Problem 21

A regular pyramid has a volume of 1152 cubic centimeters and a height of 8.64 centimeters. The base is a square. Determine the length of a base side.

Amrita Bhasin

Numerade Educator

01:10

Problem 22

Find the base diameter of a right circular cone that has a volume of 922.4 cubic centimeters and a height of 14.85 centimeters.

Trinity Steen

Numerade Educator

01:15

Problem 23

A steel forging in the shape of a regular pyramid weighs 204.8 pounds. The base of the pyramid is a square with 9.71 -inch sides. Compute the height of the forging. The steel in the forging weighs 490.5 pounds per cubic foot.

Matthew Biollo

Numerade Educator

00:41

Problem 24

The volume of a regular pyramid with an equilateral triangle base is 3174 cubic centimeters. The pyramid height is 16.91 centimeters. Find the length of each side of the triangular base.

Jay Patel

Numerade Educator

02:12

Problem 25

The frustum of a right circular cone has the larger base area equal to 31.76 square inches and the smaller base area equal to 14.05 square inches. The height is 16.29 inches. Compute the volume. Round the answer to the nearest cubic inch.

Barsha Rana

Numerade Educator

02:00

Problem 26

The container is in the shape of a frustum of a right circular cone. The smaller base area is 426 square centimeters and the larger base area is 876 square centimeters. The height is 29.5 centimeters. Compute the capacity of the container in liters. One liter contains 1000 cubic centimeters. Round the answers to the nearest tenth liter.

James Kiss

Numerade Educator

Problem 27

A steel forging is in the shape of a frustum of a regular pyramid. It has a larger base area of 58.30 square inches and a smaller base area of 40.0 square inches. The height is 5.10 inches. Find the weight of the forging. The steel weighs 490.3 pounds per cubic foot. Round the answer to the nearest tenth pound.

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00:54

Problem 28

Find the volume of the frustum of a right circular cone with a 155.68 -centimeter radius base and a 126.98 -centimeter radius base. The frustum height is 24.52 centimeters. Round the answer to the nearest hundredth cubic meter.

Melissa Stefan

Numerade Educator

02:37

Problem 29

A hollow aluminum casting in the shape of a frustum of a regular pyramid with square bases is shown. All given dimensions are outside dimensions. The casting wall thickness is 0.62 centimeter. Find the number of cubic centimeters of material that can be held in the casting. Round the answer to the nearest cubic centimeter.

James Kiss

Numerade Educator

02:37

Problem 30

The side view of a tapered steel shaft is shown. The length of the shaft is reduced from 18.40 inches to 13.60 inches. How many cubic inches of stock are removed? Round the answer to 1 decimal place.

James Kiss

Numerade Educator

02:07

Problem 31

A zinc casting is in the shape of a frustum of a right circular cone. The larger base area is 2.80 inches in diameter and the smaller base area is 2.30 inches in diameter. The height is 3.50 inches. Round the answers for $\mathrm{a}$ and $\mathrm{b}$ to 1 decimal point.
a. Compute the volume of the casting.
b. Determine the weight of the casting. Zinc weighs 0.256 pound per cubic inch.

Manisha Sarker

Numerade Educator

00:42

Problem 32

A piece in the shape of a frustum of a pyramid with regular octagon bases is 23.84 centimeters high. The length of each side of the larger base is 8.17 centimeters, and the length of each side of the smaller base is 6.77 centimeters. If a side (s) of a regular octagon is known, its area $(A)$ can be computed by the formula $A \approx 4.828 s^2$. Determine the volume of the piece. Round the answer to the nearest cubic centimeter.

Mitchell Riley

Numerade Educator

01:06

Problem 33

Find the volume of a hollow machined steel piece shown. Round the answer to 1 decimal place.

Suzanne W.

Numerade Educator

05:12

Problem 34

Parts are to be produced in the shape of a frustum of a regular pyramid with triangular bases. The larger base is to have each side 6.77 inches long and the smaller base is to have each side 4.98 inches long. Each part is to contain 240.5 cubic inches. Determine the required height. Round the answer to 2 decimal places.

Sheryl Stone

Numerade Educator