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Mathematics for Machine Technology

John C. Peterson, Robert D. Smith

Chapter 61

Areas of Circles, Sectors, and Segments - all with Video Answers

Educators

Chapter Questions

03:12

Problem 1

Plans call for triangle $\triangle B C D$ to be sheared off a corner of a rectangle as shown in the figure. A decision is made to move one vertex of the triangle $1.5 \mathrm{in}$. from $B$ to $B^{\prime}$ and the other vertex from $D$ to $D^{\prime}$. How much larger is the area of $A B^{\prime} D^{\prime} E F$ than $A B D E F$ ?

Heather Zimmers
Heather Zimmers
Numerade Educator
01:28

Problem 2

Find the area of the shaded portion of this figure. Round your answer to 2 decimal places.

Jonathon Brumley
Jonathon Brumley
Numerade Educator
02:11

Problem 3

Four circles are equally spaced on a bolt circle $3.5 \mathrm{in}$. in diameter. Use construction techniques to lay out the centers for the holes.

Madi Sousa
Madi Sousa
Numerade Educator
01:58

Problem 4

What is the radius of a circle with a circumference of $27.36 \mathrm{~cm}$. Round the answer to 2 decimal places.

Supratim Roy
Supratim Roy
Numerade Educator
00:27

Problem 5

What is the supplement of a $175^{\circ} 48^{\prime} 29^{\prime \prime}$ angle?

Liuxi Sun
Liuxi Sun
Numerade Educator
00:28

Problem 6

Solve for $h$ in the equation $Y=\sqrt{h^2-\frac{d^2}{9}}$ if $Y=24.800$ and $d=46.8$.

Lily An
Lily An
Numerade Educator
02:41

Problem 7

Find the unknown area, radius, or diameter for each of the circles 7 through 18 . Where necessary, round the answers to 1 decimal place.
$$
\begin{array}{|c|c|c|}
\hline \text { Radius } & \text { Diameter } & \text { Area } \\
\hline 7.000 \mathrm{in} . & - & \\
\hline
\end{array}
$$

Matthew Biollo
Matthew Biollo
Numerade Educator

Problem 8

Find the unknown area, radius, or diameter for each of the circles 7 through 18 . Where necessary, round the answers to 1 decimal place.
$$
\begin{array}{|c|c|c|}
\hline \text { Radius } & \text { Diameter } & \text { Area } \\
\hline 10.80 \mathrm{~cm} & - & \\
\hline
\end{array}
$$

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01:16

Problem 9

Find the unknown area, radius, or diameter for each of the circles 7 through 18 . Where necessary, round the answers to 1 decimal place.
$$
\begin{array}{|c|c|c|}
\hline \text { Radius } & \text { Diameter } & \text { Area } \\
\hline- & 15.5 \mathrm{in} . & \\
\hline
\end{array}
$$

Christopher Stanley
Christopher Stanley
Numerade Educator

Problem 10

Find the unknown area, radius, or diameter for each of the circles 7 through 18 . Where necessary, round the answers to 1 decimal place.
$$
\begin{array}{|c|c|c|}
\hline \text { Radius } & \text { Diameter } & \text { Area } \\
\hline- & 17.23 \mathrm{~mm} & \\
\hline
\end{array}
$$

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Problem 11

Find the unknown area, radius, or diameter for each of the circles 7 through 18 . Where necessary, round the answers to 1 decimal place.
$$
\begin{array}{|c|c|c|}
\hline \text { Radius } & \text { Diameter } & \text { Area } \\
\hline & - & 3.4 \mathrm{sq} \mathrm{ft} \\
\hline
\end{array}
$$

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02:39

Problem 12

Find the unknown area, radius, or diameter for each of the circles 7 through 18 . Where necessary, round the answers to 1 decimal place.
$$
\begin{array}{|c|c|c|}
\hline \text { Radius } & \text { Diameter } & \text { Area } \\
\hline- & & 218.3 \mathrm{~cm}^2 \\
\hline
\end{array}
$$

Matthew Biollo
Matthew Biollo
Numerade Educator

Problem 13

Find the unknown area, radius, or diameter for each of the circles 7 through 18 . Where necessary, round the answers to 1 decimal place.
$$
\begin{array}{|c|c|c|}
\hline \text { Radius } & \text { Diameter } & \text { Area } \\
\hline & - & 380.0 \mathrm{~mm}^2 \\
\hline
\end{array}
$$

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Problem 14

Find the unknown area, radius, or diameter for each of the circles 7 through 18 . Where necessary, round the answers to 1 decimal place.
$$
\begin{array}{|c|c|c|}
\hline \text { Radius } & \text { Diameter } & \text { Area } \\
\hline 2.78 \mathrm{in} . & - & \\
\hline
\end{array}
$$

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Problem 15

Find the unknown area, radius, or diameter for each of the circles 7 through 18 . Where necessary, round the answers to 1 decimal place.
$$
\begin{array}{|c|c|c|}
\hline \text { Radius } & \text { Diameter } & \text { Area } \\
\hline- & 0.75 \mathrm{ft} & \\
\hline
\end{array}
$$

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Problem 16

Find the unknown area, radius, or diameter for each of the circles 7 through 18 . Where necessary, round the answers to 1 decimal place.
$$
\begin{array}{|c|c|c|}
\hline \text { Radius } & \text { Diameter } & \text { Area } \\
\hline- & & 102.6 \mathrm{~cm}^2 \\
\hline
\end{array}
$$

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Problem 17

Find the unknown area, radius, or diameter for each of the circles 7 through 18 . Where necessary, round the answers to 1 decimal place.
$$
\begin{array}{|c|c|c|}
\hline \text { Radius } & \text { Diameter } & \text { Area } \\
\hline & - & 36.8 \mathrm{sq} \mathrm{in} . \\
\hline
\end{array}
$$

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Problem 18

Find the unknown area, radius, or diameter for each of the circles 7 through 18 . Where necessary, round the answers to 1 decimal place.
$$
\begin{array}{|c|c|c|}
\hline \text { Radius } & \text { Diameter } & \text { Area } \\
\hline 0.026 \mathrm{~m} & - & \\
\hline
\end{array}
$$

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01:09

Problem 19

A rectangular steel plate 15.10 inches long and 12.45 inches wide weighs 19.4 pounds. Find the weight of the plate after three 4.65 -inch diameter holes are cut. Round the answer to the nearest tenth pound.

Katelyn Chen
Katelyn Chen
Numerade Educator
01:10

Problem 20

Hydraulic pressure of 705.0 pounds per square inch is exerted on a 3.150 -inch diameter piston. Find the total force exerted on the piston. Round the answer to the nearest pound.

Ajay Singhal
Ajay Singhal
Numerade Educator

Problem 21

A circular base is shown. The base is cut from a steel plate that weighs 34 kilograms per square meter of surface area. Find the weight of the circular base. Round the answer to the nearest tenth kilogram.

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01:49

Problem 22

Find the area of the template shown. Round the answer to the nearest tenth inch. All dimensions are in inches.

Dawn Getman
Dawn Getman
Numerade Educator
01:11

Problem 23

A force of 62,125 pounds pulls on a steel rod that has a diameter of 1800 inches. Find the force pulling on 1 square inch of the cross-sectional area. Round the answer to the nearest pound.

Carson Merrill
Carson Merrill
Numerade Educator
01:20

Problem 24

A piece shown by the shaded portion is to be cut from a square plate 128 millimeters on a side.
a. Compute the area of the piece to be cut. Round the answer to the nearest square millimeter.
b. After cutting the piece, determine the percentage of the plate that will be wasted.

Vicki Stebbins
Vicki Stebbins
Numerade Educator
01:59

Problem 25

Find the unknown area, radius, or central angle for each of these sectors 25 through 36 . Where necessary, round the answers to 1 decimal place.
$$
\begin{array}{|c|c|c|}
\hline \text { Radius } & \begin{array}{c}
\text { Central } \\
\text { Angle }
\end{array} & \text { Area } \\
\hline 10.00 \mathrm{~cm} & 120.0^{\circ} & \\
\hline
\end{array}
$$

Gregory Higby
Gregory Higby
Numerade Educator
00:29

Problem 26

Find the unknown area, radius, or central angle for each of these sectors 25 through 36 . Where necessary, round the answers to 1 decimal place.
$$
\begin{array}{|c|c|c|}
\hline \text { Radius } & \begin{array}{c}
\text { Central } \\
\text { Angle }
\end{array} & \text { Area } \\
\hline 3.5 \mathrm{ft} & 90.0^{\circ} & \\
\hline
\end{array}
$$

Amy Jiang
Amy Jiang
Numerade Educator

Problem 27

Find the unknown area, radius, or central angle for each of these sectors 25 through 36 . Where necessary, round the answers to 1 decimal place.
$$
\begin{array}{|c|c|c|}
\hline \text { Radius } & \begin{array}{c}
\text { Central } \\
\text { Angle }
\end{array} & \text { Area } \\
\hline 15.3 \mathrm{in} . & 40.00^{\circ} & \\
\hline
\end{array}
$$

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Problem 28

Find the unknown area, radius, or central angle for each of these sectors 25 through 36 . Where necessary, round the answers to 1 decimal place.
$$
\begin{array}{|c|c|c|}
\hline \text { Radius } & \begin{array}{c}
\text { Central } \\
\text { Angle }
\end{array} & \text { Area } \\
\hline & 65.0^{\circ} & 300.0 \mathrm{sq} \mathrm{in.} \\
\hline
\end{array}
$$

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Problem 29

Find the unknown area, radius, or central angle for each of these sectors 25 through 36 . Where necessary, round the answers to 1 decimal place.
$$
\begin{array}{|c|c|c|}
\hline \text { Radius } & \begin{array}{c}
\text { Central } \\
\text { Angle }
\end{array} & \text { Area } \\
\hline & 180.5^{\circ} & 750.0 \mathrm{~mm}^2 \\
\hline
\end{array}
$$

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Problem 30

Find the unknown area, radius, or central angle for each of these sectors 25 through 36 . Where necessary, round the answers to 1 decimal place.
$$
\begin{array}{|c|c|c|}
\hline \text { Radius } & \begin{array}{c}
\text { Central } \\
\text { Angle }
\end{array} & \text { Area } \\
\hline9.570 \mathrm{in} . & & 94.62 \mathrm{sq} \mathrm{in} . \\
\hline
\end{array}
$$

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Problem 31

Find the unknown area, radius, or central angle for each of these sectors 25 through 36 . Where necessary, round the answers to 1 decimal place.
$$
\begin{array}{|c|c|c|}
\hline \text { Radius } & \begin{array}{c}
\text { Central } \\
\text { Angle }
\end{array} & \text { Area } \\
\hline 20.25 \mathrm{in} . & & 1028 \mathrm{sq} \mathrm{in.} \\
\hline
\end{array}
$$

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01:59

Problem 32

Find the unknown area, radius, or central angle for each of these sectors 25 through 36 . Where necessary, round the answers to 1 decimal place.
$$
\begin{array}{|c|c|c|}
\hline \text { Radius } & \begin{array}{c}
\text { Central } \\
\text { Angle }
\end{array} & \text { Area } \\
\hline 0.2 \mathrm{~m} & 220^{\circ} & \\
\hline
\end{array}
$$

Gregory Higby
Gregory Higby
Numerade Educator

Problem 33

Find the unknown area, radius, or central angle for each of these sectors 25 through 36 . Where necessary, round the answers to 1 decimal place.
$$
\begin{array}{|c|c|c|}
\hline \text { Radius } & \begin{array}{c}
\text { Central } \\
\text { Angle }
\end{array} & \text { Area } \\
\hline 54.08 \mathrm{~cm} & 26.30^{\circ} & \\
\hline
\end{array}
$$

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Problem 34

Find the unknown area, radius, or central angle for each of these sectors 25 through 36 . Where necessary, round the answers to 1 decimal place.
$$
\begin{array}{|c|c|c|}
\hline \text { Radius } & \begin{array}{c}
\text { Central } \\
\text { Angle }
\end{array} & \text { Area } \\
\hline & 307.2^{\circ} & 79.4 \mathrm{sq} \mathrm{in.} \\
\hline
\end{array}
$$

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Problem 35

Find the unknown area, radius, or central angle for each of these sectors 25 through 36 . Where necessary, round the answers to 1 decimal place.
$$
\begin{array}{|c|c|c|}
\hline \text { Radius } & \begin{array}{c}
\text { Central } \\
\text { Angle }
\end{array} & \text { Area } \\
\hline 3.273 \mathrm{in} . & & 15.882 \mathrm{sq} \mathrm{in.} \\
\hline
\end{array}
$$

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Problem 36

Find the unknown area, radius, or central angle for each of these sectors 25 through 36 . Where necessary, round the answers to 1 decimal place.
$$
\begin{array}{|c|c|c|}
\hline \text { Radius } & \begin{array}{c}
\text { Central } \\
\text { Angle }
\end{array} & \text { Area } \\
\hline 150.78 \mathrm{~mm} & 15.286^{\circ} & \\
\hline
\end{array}
$$

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02:04

Problem 37

A cross section of a piece of round stock with a V-groove cut is shown. Find the crosssectional area of the stock. Round the answer to the nearest square millimeter.

Chris Bolognese
Chris Bolognese
Numerade Educator
06:57

Problem 38

Three pieces, each in the shape of a sector, are cut from the rectangular sheet of steel shown. How many square meters are wasted after the three pieces are cut? Round the answer to the nearest tenth meter.

Sanu Kumar
Sanu Kumar
Numerade Educator
01:49

Problem 39

Determine the cross-sectional area of the machined part shown. Dimensions are in inches. Round the answer to the nearest tenth square inch.

Dawn Getman
Dawn Getman
Numerade Educator
01:28

Problem 40

Find the area of the top view of the piece shown. Dimensions are in inches. Round the answer to 1 decimal place.

Jonathon Brumley
Jonathon Brumley
Numerade Educator
02:39

Problem 41

Find the area of each of the segments $A C B$ for Exercises 41 through 45.
$$
\begin{array}{|c|c|c|}
\hline \begin{array}{c}
\text { Area of Isosceles } \\
\Delta A O B
\end{array} & \begin{array}{c}
\text { Area of Sector } \\
O A C B
\end{array} & \begin{array}{c}
\text { Area of Segment } \\
A C B
\end{array} \\
\hline 1.65 \mathrm{sq} \mathrm{ft} & 2.48 \mathrm{sq} \mathrm{ft} & \\
\hline
\end{array}
$$

Linda Hand
Linda Hand
Numerade Educator
04:55

Problem 42

Find the area of each of the segments $A C B$ for Exercises 41 through 45.
$$
\begin{array}{|c|c|c|}
\hline \begin{array}{c}
\text { Area of Isosceles } \\
\Delta A O B
\end{array} & \begin{array}{c}
\text { Area of Sector } \\
O A C B
\end{array} & \begin{array}{c}
\text { Area of Segment } \\
A C B
\end{array} \\
\hline 6.98 \mathrm{sq} \mathrm{in.} & 9.35 \mathrm{sq} \mathrm{in.} & \\
\hline
\end{array}
$$

Subham Jyoti Mishra
Subham Jyoti Mishra
Numerade Educator
04:55

Problem 43

Find the area of each of the segments $A C B$ for Exercises 41 through 45.
$$
\begin{array}{|c|c|c|}
\hline \begin{array}{c}
\text { Area of Isosceles } \\
\Delta A O B
\end{array} & \begin{array}{c}
\text { Area of Sector } \\
O A C B
\end{array} & \begin{array}{c}
\text { Area of Segment } \\
A C B
\end{array} \\
\hline 156 \mathrm{~mm}^2 & 213.5 \mathrm{~mm}^2 & \\
\hline
\end{array}
$$

Subham Jyoti Mishra
Subham Jyoti Mishra
Numerade Educator
04:55

Problem 44

Find the area of each of the segments $A C B$ for Exercises 41 through 45.
$$
\begin{array}{|c|c|c|}
\hline \begin{array}{c}
\text { Area of Isosceles } \\
\Delta A O B
\end{array} & \begin{array}{c}
\text { Area of Sector } \\
O A C B
\end{array} & \begin{array}{c}
\text { Area of Segment } \\
A C B
\end{array} \\
\hline 85.33 \mathrm{sq} \mathrm{in} . & 109.27 \mathrm{sq} \mathrm{in} . & \\
\hline
\end{array}
$$

Subham Jyoti Mishra
Subham Jyoti Mishra
Numerade Educator
04:55

Problem 45

Find the area of each of the segments $A C B$ for Exercises 41 through 45.
$$
\begin{array}{|c|c|c|}
\hline \begin{array}{c}
\text { Area of Isosceles } \\
\Delta A O B
\end{array} & \begin{array}{c}
\text { Area of Sector } \\
O A C B
\end{array} & \begin{array}{c}
\text { Area of Segment } \\
A C B
\end{array} \\
\hline 0.26 \mathrm{~m}^2 & 0.39 \mathrm{~m}^2 & \\
\hline
\end{array}
$$

Subham Jyoti Mishra
Subham Jyoti Mishra
Numerade Educator
02:03

Problem 46

Find the area of the shaded segment shown. Round the answer to 1 decimal place.

Trinity Steen
Trinity Steen
Numerade Educator
01:28

Problem 47

Compute the area of the steel insert (shaded segment) shown. Round the answer to 1 decimal place.

Jonathon Brumley
Jonathon Brumley
Numerade Educator
07:58

Problem 48

A pattern is shown.
a. Find the surface area of the pattern. Round the answer to the nearest square centimeter.
b. The metal from which the pattern is made weighs 7.85 kilograms per square meter of area. Find the weight of the pattern. Round the answer to the nearest hundredth kilogram.

Debasish Das
Debasish Das
Numerade Educator
01:39

Problem 49

The shaded piece shown is cut from a circular disk. Find the area of the piece. Round the answer to 1 decimal place. Dimensions are in inches.

Ashley High
Ashley High
Numerade Educator
01:48

Problem 50

a. Determine the area of this template after the five semicircles have been removed. Round the answer to the nearest thousandth square millimeter.
b. Calculate to the nearest whole number the percent waste due to the removal of the semicircles.

Jay Patel
Jay Patel
Numerade Educator