Question 1

Complete the table using the formula s = rΘ (Θ in radians).
  $\begin{array} { | c | c | c | } 
\hline \text { Radius, } r & \text { Angle, } \Theta & \text { Distance, } s \
\hline 15 \mathrm {~cm} & \mathrm { rad } & ----\mathrm { cm } \
\hline 12 \mathrm {~cm} & \mathrm { rad } & ----\mathrm { cm } \
\hline
\end{array}$

Accepted Answer

The answer of Complete the table using the formula s...

Question 2

Use the rules for working with measurements.
The circumference of a circle is 70.8 m. Find its radius.
r = __________ m

Accepted Answer

The answer of Use the rules for working with measurements.
The...

Question 3

Follow the rules for working with measurements. A triangular display pedestal is to be made of corrugated paper. Using the following, what size sheet needs to be designated on the drawing?

Accepted Answer

A)  15' 1" $ ×$ 15' 1" 
B)  18' 1" $ ×$ 13' 8" 
C)  18' 1" $ ×$ 13' 4" 
D)  15' 1" $ ×$ 13' 8" 
E)  15' 1" $ ×$ 13' 4" 
A)  15' 1" $ ×$ 15' 1" 
B)  18' 1" $ ×$ 13' 8" 
C)  18' 1" $ ×$ 13' 4" 
D)  15' 1" $ ×$ 13' 8" 
E)  15' 1" $ ×$ 13' 4"

Question 4

The base of a window is 7.7 m above the ground. The lower end of a ladder is 3.7 m from the side of the house. How long must a ladder be to reach the base of the window? Use the rules for working with measurements.

Accepted Answer

A)  6.3 m 
B)  5.2 m 
C)  8.5 m 
D)  11.4 m 
E)  9.6 m 
A)  6.3 m 
B)  5.2 m 
C)  8.5 m 
D)  11.4 m 
E)  9.6 m

Question 5

Complete the table using the formula s = rΘ (Θ in radians). Give your answer to three significant digits.
  $\begin{array} { | c | r | c | } 
\hline \text { Radius, } r & \text { Angle, } \Theta & \text { Distance, } s \
\hline 10 \mathrm {~cm} & ---\mathrm { rad } & 29 \mathrm {~cm} \
\hline 12 \mathrm {~mm} & ---\mathrm { rad } & 16.8 \mathrm {~mm} \
\hline
\end{array}$

Accepted Answer

The answer of Complete the table using the formula s...

Question 6

How many square feet of sheet metal are needed for the sides of the cylindrical tank shown in the illustration? (Allow 3 in. for seam overlap.)

Accepted Answer

A)  49 ft 2 
B)  94 ft 2 
C)  120 ft 2 
D)  97 ft 2 
E)  190 ft 2 
A)  49 ft 2 
B)  94 ft 2 
C)  120 ft 2 
D)  97 ft 2 
E)  190 ft 2

Question 7

A boiler 4 ft in diameter is to be placed in a corner of a room shown in Illustration. How far from corner C are points A and B of the boiler? How long is a pipe from C to the center of the boiler M ? Round your answer to the nearest hundredth.

Accepted Answer

A)  CA = CB = 6 ft, CM = 3 ft. 
B)  CA = CB = 4 ft, CM = 4 ft. 
C)  CA = CB = 8 ft, CM = 8 ft. 
D)  CA = CB = 2 ft, CM = 2.83 ft. 
E)  CA = CB = 4 ft, CM = 8 ft. 
A)  CA = CB = 6 ft, CM = 3 ft. 
B)  CA = CB = 4 ft, CM = 4 ft. 
C)  CA = CB = 8 ft, CM = 8 ft. 
D)  CA = CB = 2 ft, CM = 2.83 ft. 
E)  CA = CB = 4 ft, CM = 8 ft.

Question 8

Find the perimeter and the area of the quadrilateral.   Perimeter = __________ in.
Area = __________ $\operatorname { in } ^ { 2 }$ .

Accepted Answer

The answer of Find the perimeter and the area of...

Question 9

Find the perimeter and the area of the quadrilateral.

Accepted Answer

A)  A = 36 cm 2 
B)  P = 34 cm 
C)  P = 17 cm 
D)  A = 71 cm 2 
E)  A = 72 cm 2
F) P = 68 cm 
A)  A = 36 cm 2 
B)  P = 34 cm 
C)  P = 17 cm 
D)  A = 71 cm 2 
E)  A = 72 cm 2
F) P = 68 cm

Question 10

Follow the rules for working with measurements. A cylindrical piece of steel is 12 in. long. Its volume is 25.2 in 3. Find its diameter.

Accepted Answer

A)  0.82 in. 
B)  3.28 in. 
C)  6.56 in. 
D)  1.64 in. 
E)  164 in. 
A)  0.82 in. 
B)  3.28 in. 
C)  6.56 in. 
D)  1.64 in. 
E)  164 in.

Question 11

Find the perimeter and the area of the quadrilateral.

Accepted Answer

A)  A = 1,680 m 2 
B)  P = 55.3 m 
C)  A = 81 m 2 
D)  A = 108 m 2 
E)  P = 48.8 m
F) P = 46.3 m 
A)  A = 1,680 m 2 
B)  P = 55.3 m 
C)  A = 81 m 2 
D)  A = 108 m 2 
E)  P = 48.8 m
F) P = 46.3 m

Question 12

In Illustration $$\overline{A B}$$ and $\overline { A C }$ are secants; $$\overline{C D}$$ and $$\overline { B F }$$ are chords. Suppose ∠DFC = $44$ °, ∠EFC = $43$ °, and $\widehat { C F }$ $= 110$ arc degrees. Find the number of arc degrees in $\widehat { B D }$ .   __________ °

Accepted Answer

The answer of In Illustration $$\overline{A B}$$ and \(\overline {...

Question 13

Find the number of radians in a central angle whose arc is $\frac { 3 } { 7 }$ of a circle.

Accepted Answer

A)  $\frac { 6 } { 7 }$ rad 
B)  $\frac { 6 } { 7 } \pi$ rad 
C)  $\frac { 7 } { 6 } \pi$ rad 
D)  $\frac { 3 } { 7 } \pi$ rad 
E)  $\frac { 2 } { 9 } \pi$ rad 
A)  $\frac { 6 } { 7 }$ rad 
B)  $\frac { 6 } { 7 } \pi$ rad 
C)  $\frac { 7 } { 6 } \pi$ rad 
D)  $\frac { 3 } { 7 } \pi$ rad 
E)  $\frac { 2 } { 9 } \pi$ rad

Question 14

The resistor current is 18 A. The total current is 39 A. Find the coil current. (See illustration.) Use the rules for working with measurements.

Accepted Answer

A)  21 A 
B)  34 A 
C)  35 A 
D)  32 A 
E)  33 A 
A)  21 A 
B)  34 A 
C)  35 A 
D)  32 A 
E)  33 A

Question 15

Find the area and perimeter of the triangle shown below. Use the rules for working with measurements.

Accepted Answer

A)  perimeter = 35.4, area = 44.1 ft 2 
B)  perimeter = 35.4, area = 46.3 ft 2 
C)  perimeter = 36.5, area = 46.3 ft 2 
D)  perimeter = 35.4, area = 48.5 ft 2 
E)  perimeter = 36.5, area = 48.5 ft 2 
A)  perimeter = 35.4, area = 44.1 ft 2 
B)  perimeter = 35.4, area = 46.3 ft 2 
C)  perimeter = 36.5, area = 46.3 ft 2 
D)  perimeter = 35.4, area = 48.5 ft 2 
E)  perimeter = 36.5, area = 48.5 ft 2

Question 16

Given $\overline { \mathrm { AB } } \| \overline { \mathrm { CD } }$ , find the measure of ?2.

Accepted Answer

A)  58° 
B)  55° 
C)  54° 
D)  60° 
E)  120° 
A)  58° 
B)  55° 
C)  54° 
D)  60° 
E)  120°

Question 17

Find the volume of the wagon box shown in the illustration below.

Accepted Answer

A)  408 ft 3 
B)  530 ft 3 
C)  306 ft 3 
D)  412 ft 3 
E)  405 ft 3 
A)  408 ft 3 
B)  530 ft 3 
C)  306 ft 3 
D)  412 ft 3 
E)  405 ft 3

Question 18

A small heater has a rectangular filter that is $13 \text { in. } \times 24 \text { in. }$ Another larger heater requires a similar filter that has a 26 in. width. What is the height of this larger filter?

Accepted Answer

A)  49 in. 
B)  48 in. 
C)  27 in. 
D)  26 in. 
E)  24 in. 
A)  49 in. 
B)  48 in. 
C)  27 in. 
D)  26 in. 
E)  24 in.

Question 19

A new metal cylindrical storage tank is to be made. If its volume is to be $2,5\bar00$ ft 3, what is the height of the tank if its radius is 7 ft? What is its total surface area? Round your answers to three significant digits.

Accepted Answer

A)  The height is 785 ft, the total surface area is 7,130 ft 2. 
B)  The height is 16.2 ft, the total surface area is 1,020 ft 2. 
C)  The height is 78.5 ft, the total surface area is 713 ft 2. 
D)  The height is 16.2 ft, the total surface area is 7,130 ft 2. 
E)  The height is 78.5 ft, the total surface area is 1,020 ft 2. 
A)  The height is 785 ft, the total surface area is 7,130 ft 2. 
B)  The height is 16.2 ft, the total surface area is 1,020 ft 2. 
C)  The height is 78.5 ft, the total surface area is 713 ft 2. 
D)  The height is 16.2 ft, the total surface area is 7,130 ft 2. 
E)  The height is 78.5 ft, the total surface area is 1,020 ft 2.

Question 20

Two pieces of steel angle are welded to form right angles. The lengths of the two pieces are 9 ft and 8 ft respectively. What is the distance between the two unwelded ends? Use the rules for working with measurements.

Accepted Answer

A)  14 ft 
B)  11 ft 
C)  12 ft 
D)  15 ft 
E)  17 ft 
A)  14 ft 
B)  11 ft 
C)  12 ft 
D)  15 ft 
E)  17 ft

Complete the table using the formula s = rΘ (Θ in radians). Radius, r Angle, \Theta Distance, s 15 ---- 12 ----

Use the rules for working with measurements. The circumference of a circle is 70.8 m. Find its radius. r = __________ m

Follow the rules for working with measurements. A triangular display pedestal is to be made of corrugated paper. Using the following, what size sheet needs to be designated on the drawing?

The base of a window is 7.7 m above the ground. The lower end of a ladder is 3.7 m from the side of the house. How long must a ladder be to reach the base of the window? Use the rules for working with measurements.

Complete the table using the formula s = rΘ (Θ in radians). Give your answer to three significant digits. Radius, r Angle, \Theta Distance, s 10 --- 29 12 --- 16.8

How many square feet of sheet metal are needed for the sides of the cylindrical tank shown in the illustration? (Allow 3 in. for seam overlap.)

A boiler 4 ft in diameter is to be placed in a corner of a room shown in Illustration. How far from corner C are points A and B of the boiler? How long is a pipe from C to the center of the boiler M ? Round your answer to the nearest hundredth.

Find the perimeter and the area of the quadrilateral. $Find the perimeter and the area of the quadrilateral. Perimeter = in. Area = \operatorname { in } ^ { 2 } .$ Perimeter = in. Area = $\operatorname { in } ^ { 2 }$ .

Find the perimeter and the area of the quadrilateral.

Follow the rules for working with measurements. A cylindrical piece of steel is 12 in. long. Its volume is 25.2 in ³. Find its diameter.

Find the perimeter and the area of the quadrilateral.

Find the number of radians in a central angle whose arc is $\frac { 3 } { 7 }$ of a circle.

The resistor current is 18 A. The total current is 39 A. Find the coil current. (See illustration.) Use the rules for working with measurements.

Find the area and perimeter of the triangle shown below. Use the rules for working with measurements.

Given $\overline { \mathrm { AB } } \| \overline { \mathrm { CD } }$ , find the measure of ?2. $Given \overline { \mathrm { AB } } \| \overline { \mathrm { CD } } , find the measure of ?2.$

Find the volume of the wagon box shown in the illustration below.

A small heater has a rectangular filter that is $13 \text { in. } \times 24 \text { in. }$ Another larger heater requires a similar filter that has a 26 in. width. What is the height of this larger filter?

A new metal cylindrical storage tank is to be made. If its volume is to be $2,5\bar00$ ft ³, what is the height of the tank if its radius is 7 ft? What is its total surface area? Round your answers to three significant digits.

Two pieces of steel angle are welded to form right angles. The lengths of the two pieces are 9 ft and 8 ft respectively. What is the distance between the two unwelded ends? Use the rules for working with measurements.

Basic Concepts

Signed Numbers and Powers of 10

The Metric System

Measurement

Polynomials: an Introduction to Algebra

Equations and Formulas

Ratio and Proportion

Graphing Linear Equations

Systems of Linear Equations

Factoring Algebraic Expressions

Quadratic Equations

Right Triangle Trigonometry

Trigonometry With Any Angle

Basic Statistics

Binary and Hexadecimal Numbers

Filters

Exam 12: Geometry

Complete the table using the formula s = rΘ (Θ in radians). Radius, r Angle, \Theta Distance, s 15 ---- 12 ----

Use the rules for working with measurements. The circumference of a circle is 70.8 m. Find its radius. r = __________ m

Follow the rules for working with measurements. A triangular display pedestal is to be made of corrugated paper. Using the following, what size sheet needs to be designated on the drawing?

The base of a window is 7.7 m above the ground. The lower end of a ladder is 3.7 m from the side of the house. How long must a ladder be to reach the base of the window? Use the rules for working with measurements.

Complete the table using the formula s = rΘ (Θ in radians). Give your answer to three significant digits. Radius, r Angle, \Theta Distance, s 10 --- 29 12 --- 16.8

How many square feet of sheet metal are needed for the sides of the cylindrical tank shown in the illustration? (Allow 3 in. for seam overlap.)

A boiler 4 ft in diameter is to be placed in a corner of a room shown in Illustration. How far from corner C are points A and B of the boiler? How long is a pipe from C to the center of the boiler M ? Round your answer to the nearest hundredth.

Find the perimeter and the area of the quadrilateral. Perimeter = __________ in. Area = __________ in⁡2\operatorname { in } ^ { 2 }in2 .

Find the perimeter and the area of the quadrilateral.

Follow the rules for working with measurements. A cylindrical piece of steel is 12 in. long. Its volume is 25.2 in 3. Find its diameter.

Find the perimeter and the area of the quadrilateral.

Find the number of radians in a central angle whose arc is 37\frac { 3 } { 7 }73​ of a circle.

The resistor current is 18 A. The total current is 39 A. Find the coil current. (See illustration.) Use the rules for working with measurements.

Find the area and perimeter of the triangle shown below. Use the rules for working with measurements.

Given AB‾∥CD‾\overline { \mathrm { AB } } \| \overline { \mathrm { CD } }AB∥CD , find the measure of ?2.

Find the volume of the wagon box shown in the illustration below.

A small heater has a rectangular filter that is 13 in. ×24 in. 13 \text { in. } \times 24 \text { in. }13 in. ×24 in. Another larger heater requires a similar filter that has a 26 in. width. What is the height of this larger filter?

A new metal cylindrical storage tank is to be made. If its volume is to be 2,50ˉ02,5\bar002,50ˉ0 ft 3, what is the height of the tank if its radius is 7 ft? What is its total surface area? Round your answers to three significant digits.

Two pieces of steel angle are welded to form right angles. The lengths of the two pieces are 9 ft and 8 ft respectively. What is the distance between the two unwelded ends? Use the rules for working with measurements.

Basic Concepts

Signed Numbers and Powers of 10

The Metric System

Measurement

Polynomials: an Introduction to Algebra

Equations and Formulas

Ratio and Proportion

Graphing Linear Equations

Systems of Linear Equations

Factoring Algebraic Expressions

Quadratic Equations

Right Triangle Trigonometry

Trigonometry With Any Angle

Basic Statistics

Binary and Hexadecimal Numbers

Filters

Find the perimeter and the area of the quadrilateral. $Find the perimeter and the area of the quadrilateral. Perimeter = in. Area = \operatorname { in } ^ { 2 } .$ Perimeter = in. Area = $\operatorname { in } ^ { 2 }$ .

Follow the rules for working with measurements. A cylindrical piece of steel is 12 in. long. Its volume is 25.2 in ³. Find its diameter.

Find the number of radians in a central angle whose arc is $\frac { 3 } { 7 }$ of a circle.

Given $\overline { \mathrm { AB } } \| \overline { \mathrm { CD } }$ , find the measure of ?2. $Given \overline { \mathrm { AB } } \| \overline { \mathrm { CD } } , find the measure of ?2.$

A small heater has a rectangular filter that is $13 \text { in. } \times 24 \text { in. }$ Another larger heater requires a similar filter that has a 26 in. width. What is the height of this larger filter?

A new metal cylindrical storage tank is to be made. If its volume is to be $2,5\bar00$ ft ³, what is the height of the tank if its radius is 7 ft? What is its total surface area? Round your answers to three significant digits.