Question 1

A wheel of diameter 6 m travels a distance of 18.26 m. Find the angle Θ in radians, to three significant digits, that the wheel turns.

Accepted Answer

A)  6.09 rad 
B)  8.09 rad 
C)  19.6 rad 
D)  3.04 rad 
E)  12.2 rad 
A)  6.09 rad 
B)  8.09 rad 
C)  19.6 rad 
D)  3.04 rad 
E)  12.2 rad

Question 2

Find the length of DE in the illustration.

Accepted Answer

A)  DE is 15.5 m 
B)  DE is 12.7 m 
C)  DE is 11.1 m 
D)  DE is 13.2 m 
E)  DE is 14.3 m 
A)  DE is 15.5 m 
B)  DE is 12.7 m 
C)  DE is 11.1 m 
D)  DE is 13.2 m 
E)  DE is 14.3 m

Question 3

A round plate $14$ in. in diameter is to have ten holes drilled through it. This is accomplished by creating a drawing for half the circle and the then "mirroring" the drawing for the other half of the circle. The $\frac { 1 } { 2 }$ in. diameter holes are to be equally spaced on a $10$ in. concentric circle in the top half of the plate. What is the angle A between the holes? What is the angle B between the horizontal and each of the end holes?

Accepted Answer

A)  A = $36$ °, B = $30$ ° 
B)  A = $72$ °, B = $36$ ° 
C)  A = $60$ °, B = $30$ ° 
D)  A = $60$ °, B = $18$ ° 
E)  A = $36$ °, B = $18$ ° 
A)  A = $36$ °, B = $30$ ° 
B)  A = $72$ °, B = $36$ ° 
C)  A = $60$ °, B = $30$ ° 
D)  A = $60$ °, B = $18$ ° 
E)  A = $36$ °, B = $18$ °

Question 4

Use the rules for working with measurements.   Find the circumference of the circle.
C = __________ m
Find the area of the circle.
A = __________ $m ^ { 2 }$

Accepted Answer

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

Question 5

You are designing a dome house in the shape of a hemisphere with a 31 ft outside diameter. Two coats of sealer are required to cover and seal the exposed external concrete. If one gallon covers 110 ft 2, how many gallons are required for the bill of materials?

Accepted Answer

A)  27 gallons 
B)  54 gallons 
C)  20 gallons 
D)  30 gallons 
E)  40 gallons 
A)  27 gallons 
B)  54 gallons 
C)  20 gallons 
D)  30 gallons 
E)  40 gallons

Question 6

Follow the rules for working with measurements.
Find the volume of the figure.   V = __________ cm3

Accepted Answer

Question 7

A tree casts a shadow $$11\bar0$$ ft long when a vertical rod 4 ft high casts a shadow 2 ft long. (See Illustration.) How tall is the tree?

Accepted Answer

A)  The tree is 260 ft long. 
B)  The tree is 220 ft long. 
C)  The tree is $22 \overline { 0 }$ ft long. 
D)  The tree is 250 ft long. 
E)  The tree is $26 \overline { 0 }$ ft long. 
A)  The tree is 260 ft long. 
B)  The tree is 220 ft long. 
C)  The tree is $22 \overline { 0 }$ ft long. 
D)  The tree is 250 ft long. 
E)  The tree is $26 \overline { 0 }$ ft long.

Question 8

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

Accepted Answer

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

Question 9

Complete the table using the formula s = rΘ (Θ in radians). $$\begin{array} { | c | c | r | } 
\hline \text { Radius, } r & \text { Angle, } \Theta & \text { Distance, } s \
\hline 11 \mathrm {~cm} & 55 ^ { \circ } &---- \mathrm { cm } \
\hline 23 \mathrm {~mm} & 40 ^ { \circ } &---- \mathrm { mm } \
\hline
\end{array}$$

Accepted Answer

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

Question 10

The resistor current is 50.2 A. The coil current is 65.6 A. Find the total current. (See illustration.) Use the rules for working with measurements.

Accepted Answer

A)  82.6 A 
B)  84.8 A 
C)  79.3 A 
D)  115.8 A 
E)  83.7 A 
A)  82.6 A 
B)  84.8 A 
C)  79.3 A 
D)  115.8 A 
E)  83.7 A

Question 11

Find the impedance of a circuit with reactance 20.8 Ω and resistance 38.6 Ω . (See illustration.) Use the rules for working with measurements.   __________ Ω

Accepted Answer

The answer of Find the impedance of a circuit with...

Question 12

The circumference of a circle is 70.7 m. Find its radius. Use the rules for working with measurements.

Accepted Answer

A)  The radius is 4.74 m. 
B)  The radius is 11.3 m. 
C)  The radius is 5.63 m. 
D)  The radius is 22.5 m. 
E)  The radius is 45.0 m. 
A)  The radius is 4.74 m. 
B)  The radius is 11.3 m. 
C)  The radius is 5.63 m. 
D)  The radius is 22.5 m. 
E)  The radius is 45.0 m.

Question 13

A 9 ft by 8 ft bookcase is to be built. It has horizontal shelves every foot. A support is to be notched in the shelves diagonally from one corner to the opposite corner. At what point should each of the shelves be notched? That is, find lengths A, B, C, D and E in the illustration. How long is the diagonal crosspiece? Round your answer to the nearest hundredth.

Accepted Answer

A)  A = 1.3 ft, B = 2.7 ft, C = 4 ft, D = 5.3 ft,E = 6.7 ft, the crosspiece is 12 ft. 
B)  A = 1.5 ft, B = 3 ft, C = 4.5 ft, D = 6 ft,E = 7.5 ft, the crosspiece is 12.04 ft. 
C)  A = 1.5 ft, B = 3 ft, C = 5.5 ft, D = 5 ft,E = 7.5 ft, the crosspiece is 12.04 ft. 
D)  A = 1.33 ft, B = 2.67 ft, C = 4 ft, D = 5.33 ft,E = 6.67 ft, the crosspiece is 12.04 ft. 
E)  A = 1.5 ft, B = 3 ft, C = 4.5 ft, D = 6 ft,E = 6.5 ft, the crosspiece is 12 ft. 
A)  A = 1.3 ft, B = 2.7 ft, C = 4 ft, D = 5.3 ft,E = 6.7 ft, the crosspiece is 12 ft. 
B)  A = 1.5 ft, B = 3 ft, C = 4.5 ft, D = 6 ft,E = 7.5 ft, the crosspiece is 12.04 ft. 
C)  A = 1.5 ft, B = 3 ft, C = 5.5 ft, D = 5 ft,E = 7.5 ft, the crosspiece is 12.04 ft. 
D)  A = 1.33 ft, B = 2.67 ft, C = 4 ft, D = 5.33 ft,E = 6.67 ft, the crosspiece is 12.04 ft. 
E)  A = 1.5 ft, B = 3 ft, C = 4.5 ft, D = 6 ft,E = 6.5 ft, the crosspiece is 12 ft.

Question 14

Suppose l||m, $\angle 1 = 8 x + 52$ , and $\angle 3 = 3 x + 62$ .  
Find the value of x.

Accepted Answer

A)  6 
B)  12 
C)  8 
D)  9 
E)  5 
A)  6 
B)  12 
C)  8 
D)  9 
E)  5

Question 15

Classify the given angle as right, acute, or obtuse.

Accepted Answer

A)  obtuse angle 
B)  right angle 
C)  acute angle 
A)  obtuse angle 
B)  right angle 
C)  acute angle

Question 16

A respirator unit needs a rectangular floor space of 0.76 m by 1.2 m. How many units could be placed in a storeroom having $6\bar0 \mathrm {~m} ^ { 2 }$ of floor space?

Accepted Answer

A)  30 
B)  68 
C)  66 
D)  33 
E)  65 
A)  30 
B)  68 
C)  66 
D)  33 
E)  65

Question 17

Find x and y to the nearest tenth using the formula s = rΘ (Θ in radians).  
Radius, r
Angle, Θ
Distance, s
20 cm
X o
20)94 cm
0)021 m
Y o
0)0205 m

Accepted Answer

A)  x = 120 o; y = 175.7 o 
B)  x = 60 o; y = 175.7 o 
C)  x = 188.5 o; y = 111.9 o 
D)  x = 60 o; y = 111.9 o 
E)  x = 60 o; y = 55.9 o 
A)  x = 120 o; y = 175.7 o 
B)  x = 60 o; y = 175.7 o 
C)  x = 188.5 o; y = 111.9 o 
D)  x = 60 o; y = 111.9 o 
E)  x = 60 o; y = 55.9 o

Question 18

Round your answers to three significant digits. A piece of 17 in. $ ×$ 14 in. metal duct is a rectangular prism. If it is 5 ft long, what is the lateral surface area A? What is its volume V?

Accepted Answer

A)  A = 3,740 in. 2, V = 14,600 in. 3 
B)  A = 3,720 in. 2, V = 1,190 in. 3 
C)  A = 37,400 in. 2, V = 14,300 in. 3 
D)  A = 3,720 in. 2, V = 146,000 in. 3 
E)  A = 3,720 in. 2, V = 14,300 in. 3 
A)  A = 3,740 in. 2, V = 14,600 in. 3 
B)  A = 3,720 in. 2, V = 1,190 in. 3 
C)  A = 37,400 in. 2, V = 14,300 in. 3 
D)  A = 3,720 in. 2, V = 146,000 in. 3 
E)  A = 3,720 in. 2, V = 14,300 in. 3

Question 19

Follow the rules for working with measurements. Gravel is piled in the shape of a cone. The circumference of the base is 200 ft. The slant height is 41 ft. If the gravel weighs 3,200 lb/yd 3, how many 22-ton truckloads are needed to transport the gravel?

Accepted Answer

A)  510 truckloads 
B)  74 truckloads 
C)  49 truckloads 
D)  86 truckloads 
E)  36 truckloads 
A)  510 truckloads 
B)  74 truckloads 
C)  49 truckloads 
D)  86 truckloads 
E)  36 truckloads

Question 20

Follow the rules for working with measurements. Find the surface area and the volume of the sphere.

Accepted Answer

A)  A = 606 m 2, V = 1,450 m 3 
B)  A = 561 m 2, V = 1,495 m 3 
C)  A = 176 m 2, V = 264 m 3 
D)  A = 646 m 2, V = 1,410 m 3 
E)  A = 616 m 2, V = 1,440 m 3 
A)  A = 606 m 2, V = 1,450 m 3 
B)  A = 561 m 2, V = 1,495 m 3 
C)  A = 176 m 2, V = 264 m 3 
D)  A = 646 m 2, V = 1,410 m 3 
E)  A = 616 m 2, V = 1,440 m 3

A wheel of diameter 6 m travels a distance of 18.26 m. Find the angle Θ in radians, to three significant digits, that the wheel turns.

Find the length of DE in the illustration.

Use the rules for working with measurements. $Use the rules for working with measurements. Find the circumference of the circle. C = m Find the area of the circle. A = m ^ { 2 }$ Find the circumference of the circle. C = m Find the area of the circle. A = $m ^ { 2 }$

You are designing a dome house in the shape of a hemisphere with a 31 ft outside diameter. Two coats of sealer are required to cover and seal the exposed external concrete. If one gallon covers 110 ft ², how many gallons are required for the bill of materials?

Follow the rules for working with measurements. Find the volume of the figure. V = __________ cm³

A tree casts a shadow $11\bar0$ ft long when a vertical rod 4 ft high casts a shadow 2 ft long. (See Illustration.) How tall is the tree? $A tree casts a shadow 11\bar0 ft long when a vertical rod 4 ft high casts a shadow 2 ft long. (See Illustration.) How tall is the tree?$

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

Complete the table using the formula s = rΘ (Θ in radians). Radius, r Angle, \Theta Distance, s 11 5 ---- 23 4 ----

The resistor current is 50.2 A. The coil current is 65.6 A. Find the total current. (See illustration.) Use the rules for working with measurements.

Find the impedance of a circuit with reactance 20.8 Ω and resistance 38.6 Ω . (See illustration.) Use the rules for working with measurements. __________ Ω

The circumference of a circle is 70.7 m. Find its radius. Use the rules for working with measurements.

Suppose l||m, $\angle 1 = 8 x + 52$ , and $\angle 3 = 3 x + 62$ . Find the value of x. $Suppose l||m, \angle 1 = 8 x + 52 , and \angle 3 = 3 x + 62 . Find the value of x.$

Classify the given angle as right, acute, or obtuse.

A respirator unit needs a rectangular floor space of 0.76 m by 1.2 m. How many units could be placed in a storeroom having $6\bar0 \mathrm {~m} ^ { 2 }$ of floor space?

Find x and y to the nearest tenth using the formula s = rΘ (Θ in radians). Radius, r Angle, Θ Distance, s 20 cm X ^o 20)94 cm 0)021 m Y ^o 0)0205 m

Round your answers to three significant digits. A piece of 17 in. $×$ 14 in. metal duct is a rectangular prism. If it is 5 ft long, what is the lateral surface area A? What is its volume V?

Follow the rules for working with measurements. Gravel is piled in the shape of a cone. The circumference of the base is 200 ft. The slant height is 41 ft. If the gravel weighs 3,200 lb/yd ³, how many 22-ton truckloads are needed to transport the gravel?

Follow the rules for working with measurements. Find the surface area and the volume of the sphere.

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

A wheel of diameter 6 m travels a distance of 18.26 m. Find the angle Θ in radians, to three significant digits, that the wheel turns.

Find the length of DE in the illustration.

Use the rules for working with measurements. Find the circumference of the circle. C = __________ m Find the area of the circle. A = __________ m2m ^ { 2 }m2

You are designing a dome house in the shape of a hemisphere with a 31 ft outside diameter. Two coats of sealer are required to cover and seal the exposed external concrete. If one gallon covers 110 ft 2, how many gallons are required for the bill of materials?

Follow the rules for working with measurements. Find the volume of the figure. V = __________ cm3

A tree casts a shadow 110ˉ11\bar0110ˉ ft long when a vertical rod 4 ft high casts a shadow 2 ft long. (See Illustration.) How tall is the tree?

Find the perimeter and the area of the quadrilateral. Perimeter = __________ m Area = __________ m2m ^ { 2 }m2

Complete the table using the formula s = rΘ (Θ in radians). Radius, r Angle, \Theta Distance, s 11 5 ---- 23 4 ----

The resistor current is 50.2 A. The coil current is 65.6 A. Find the total current. (See illustration.) Use the rules for working with measurements.

Find the impedance of a circuit with reactance 20.8 Ω and resistance 38.6 Ω . (See illustration.) Use the rules for working with measurements. __________ Ω

The circumference of a circle is 70.7 m. Find its radius. Use the rules for working with measurements.

Suppose l||m, ∠1=8x+52\angle 1 = 8 x + 52∠1=8x+52 , and ∠3=3x+62\angle 3 = 3 x + 62∠3=3x+62 . Find the value of x.

Classify the given angle as right, acute, or obtuse.

A respirator unit needs a rectangular floor space of 0.76 m by 1.2 m. How many units could be placed in a storeroom having 60ˉ m26\bar0 \mathrm {~m} ^ { 2 }60ˉ m2 of floor space?

Find x and y to the nearest tenth using the formula s = rΘ (Θ in radians). Radius, r Angle, Θ Distance, s 20 cm X o 20)94 cm 0)021 m Y o 0)0205 m

Round your answers to three significant digits. A piece of 17 in. × ×× 14 in. metal duct is a rectangular prism. If it is 5 ft long, what is the lateral surface area A? What is its volume V?

Follow the rules for working with measurements. Gravel is piled in the shape of a cone. The circumference of the base is 200 ft. The slant height is 41 ft. If the gravel weighs 3,200 lb/yd 3, how many 22-ton truckloads are needed to transport the gravel?

Follow the rules for working with measurements. Find the surface area and the volume of the sphere.

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

Use the rules for working with measurements. $Use the rules for working with measurements. Find the circumference of the circle. C = m Find the area of the circle. A = m ^ { 2 }$ Find the circumference of the circle. C = m Find the area of the circle. A = $m ^ { 2 }$

You are designing a dome house in the shape of a hemisphere with a 31 ft outside diameter. Two coats of sealer are required to cover and seal the exposed external concrete. If one gallon covers 110 ft ², how many gallons are required for the bill of materials?

Follow the rules for working with measurements. Find the volume of the figure. V = __________ cm³

A tree casts a shadow $11\bar0$ ft long when a vertical rod 4 ft high casts a shadow 2 ft long. (See Illustration.) How tall is the tree? $A tree casts a shadow 11\bar0 ft long when a vertical rod 4 ft high casts a shadow 2 ft long. (See Illustration.) How tall is the tree?$

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

Suppose l||m, $\angle 1 = 8 x + 52$ , and $\angle 3 = 3 x + 62$ . Find the value of x. $Suppose l||m, \angle 1 = 8 x + 52 , and \angle 3 = 3 x + 62 . Find the value of x.$

A respirator unit needs a rectangular floor space of 0.76 m by 1.2 m. How many units could be placed in a storeroom having $6\bar0 \mathrm {~m} ^ { 2 }$ of floor space?

Find x and y to the nearest tenth using the formula s = rΘ (Θ in radians). Radius, r Angle, Θ Distance, s 20 cm X ^o 20)94 cm 0)021 m Y ^o 0)0205 m

Round your answers to three significant digits. A piece of 17 in. $×$ 14 in. metal duct is a rectangular prism. If it is 5 ft long, what is the lateral surface area A? What is its volume V?

Follow the rules for working with measurements. Gravel is piled in the shape of a cone. The circumference of the base is 200 ft. The slant height is 41 ft. If the gravel weighs 3,200 lb/yd ³, how many 22-ton truckloads are needed to transport the gravel?