Question 1

Find the measure of the unknown angle.

Accepted Answer

A)  x = 129.3° 
B)  x = 30.1° 
C)  x = 64.7° 
D)  x = 137.3° 
E)  x = 63.3° 
A)  x = 129.3° 
B)  x = 30.1° 
C)  x = 64.7° 
D)  x = 137.3° 
E)  x = 63.3°

Question 2

Suppose l||m, $\angle 1 = 3 x - 50$ and $\angle 2 = x + 56$ .  
Find the value of x.

Accepted Answer

A)  58 
B)  38 
C)  53 
D)  106 
E)  63 
A)  58 
B)  38 
C)  53 
D)  106 
E)  63

Question 3

Follow the rules for working with measurements. Find the volume of the gravity bin shown in the illustration below.

Accepted Answer

A)  244 ft 3 
B)  42.5 ft 3 
C)  188 ft 3 
D)  187 ft 3 
E)  190 ft 3 
A)  244 ft 3 
B)  42.5 ft 3 
C)  188 ft 3 
D)  187 ft 3 
E)  190 ft 3

Question 4

Following the rules for working with measurements, find the area of the lateral surface to be painted in the illustration. Assume there are no windows.

Accepted Answer

A)  2,180 m 2 
B)  2,230 m 2 
C)  2,330 m 2 
D)  3,230 m 2 
E)  558 m 2 
A)  2,180 m 2 
B)  2,230 m 2 
C)  2,330 m 2 
D)  3,230 m 2 
E)  558 m 2

Question 5

Looking at the side of a welding metal storage bin, the shape is a trapezoid. The lengths of the bases are 58.8 cm and 62.0 cm, and the height is 48.8 cm. Find its area.

Accepted Answer

A)  $\text { Area } = 2,990 \mathrm {~cm} ^ { 2 }$ 
B)  $\text { Area } = 3,020 \mathrm {~cm} ^ { 2 }$ 
C)  $\text { Area } = 3,250 \mathrm {~cm} ^ { 2 }$ 
D)  $\text { Area } = 2,950 \mathrm {~cm} ^ { 2 }$ 
E)  $\text { Area } = 2,947 \mathrm {~cm} ^ { 2 }$ 
A)  $\text { Area } = 2,990 \mathrm {~cm} ^ { 2 }$ 
B)  $\text { Area } = 3,020 \mathrm {~cm} ^ { 2 }$ 
C)  $\text { Area } = 3,250 \mathrm {~cm} ^ { 2 }$ 
D)  $\text { Area } = 2,950 \mathrm {~cm} ^ { 2 }$ 
E)  $\text { Area } = 2,947 \mathrm {~cm} ^ { 2 }$

Question 6

Follow the rules for working with measurements. A steel rod of a cross-sectional area 4 in. 2 weighs 32 lb. Find its length. (Steel weighs 0.28 lb/in 3.)

Accepted Answer

A)  700 in. 
B)  29 in. 
C)  35 in. 
D)  350 in. 
E)  38 in. 
A)  700 in. 
B)  29 in. 
C)  35 in. 
D)  350 in. 
E)  38 in.

Question 7

Find the length of the hypotenuse in the triangle. Use the rules for working with measurements.   c = __________ cm

Accepted Answer

The answer of Find the length of the hypotenuse in...

Question 8

Follow the rules for working with measurements.
Find the volume of the figure.   V = __________ in3.

Accepted Answer

Question 9

Follow the rules for working with measurements. Two different sizes of square metal duct are joined by a piece that is a frustum of a pyramid. Find the lateral surface area, if the small end is square with one side of length 17 in. and the larger square end is of length 19 in. on one side with a slant height of 2 in.

Accepted Answer

A)  A = 141 in. 2 
B)  A = 288 in. 2 
C)  A = 144 in. 2 
D)  A = 151 in. 2 
E)  A = 132 in. 2 
A)  A = 141 in. 2 
B)  A = 288 in. 2 
C)  A = 144 in. 2 
D)  A = 151 in. 2 
E)  A = 132 in. 2

Question 10

Follow the rules for working with measurements. Find the volume of the figure.

Accepted Answer

A)  V = 11,400,000 mm 3 
B)  V = 63,500 mm 3 
C)  V = 154,000 mm 3 
D)  V = 75,800 mm 3 
E)  V = 22,400 mm 3 
A)  V = 11,400,000 mm 3 
B)  V = 63,500 mm 3 
C)  V = 154,000 mm 3 
D)  V = 75,800 mm 3 
E)  V = 22,400 mm 3

Question 11

Follow the rules for working with measurements. Find the volume and lateral surface area of the frustum of the cone shown in the illustration.

Accepted Answer

A)  A = 14,540 ft 2 
B)  A = 6,210 ft 2 
C)  V = 28,300 ft 3 
D)  V = 6,400 ft 3 
E)  A = 880 ft 2
F) V = 74,000 ft 3
G) V = 61,700 ft 3
H) A = 3,090 ft 2 
A)  A = 14,540 ft 2 
B)  A = 6,210 ft 2 
C)  V = 28,300 ft 3 
D)  V = 6,400 ft 3 
E)  A = 880 ft 2
F) V = 74,000 ft 3
G) V = 61,700 ft 3
H) A = 3,090 ft 2

Question 12

A plumber wishes to add a pipe parallel to an existing pipe as shown in the illustration. Find angle x.

Accepted Answer

A)  35° 
B)  290° 
C)  145° 
D)  55° 
E)  125° 
A)  35° 
B)  290° 
C)  145° 
D)  55° 
E)  125°

Question 13

An experimental balloon is to have a diameter of 5.68 m. How much material is needed for this balloon?

Accepted Answer

A)  143 m 2 
B)  23 m 2 
C)  101 m 2 
D)  25.3 m 2 
E)  71.4 m 2 
A)  143 m 2 
B)  23 m 2 
C)  101 m 2 
D)  25.3 m 2 
E)  71.4 m 2

Question 14

Follow the rules for working with measurements. A steel cylindrical tank must hold 8,500 gal of dyed water for a cloth process. Due to space constraints, the cylindrical tank is made 11 ft in diameter. How tall must the tank be? (Water weighs 8.34 lb/gal and 62.4 lb/ft 3.)

Accepted Answer

A)  47.8 ft 
B)  0.598 ft 
C)  23.9 ft 
D)  12 ft 
E)  118 ft 
A)  47.8 ft 
B)  0.598 ft 
C)  23.9 ft 
D)  12 ft 
E)  118 ft

Question 15

A plumber wishes to add a pipe parallel to an existing pipe as shown in illustration. Find angle x.   __________ $^ { \circ }$

Accepted Answer

The answer of A plumber wishes to add a pipe...

Question 16

Following the rules for working with measurements find the lateral surface area of the rectangular prism shown in the illustration above A L, the total surface area of the prism A T and the volume of the prism V.

Accepted Answer

A)  A L = 256 m 2, A T = 512 m 2, V = 512 m 3 
B)  A L = 256 m 2, A T = 384 m 2, V = 512 m 3 
C)  A L = 388 m 2, A T = 256 m 2, V = 510 m 3 
D)  A L = 388 m 2, A T = 256 m 2, V = 512 m 3 
E)  A L = 384 m 2, A T = 256 m 2, V = 512 m 3 
A)  A L = 256 m 2, A T = 512 m 2, V = 512 m 3 
B)  A L = 256 m 2, A T = 384 m 2, V = 512 m 3 
C)  A L = 388 m 2, A T = 256 m 2, V = 510 m 3 
D)  A L = 388 m 2, A T = 256 m 2, V = 512 m 3 
E)  A L = 384 m 2, A T = 256 m 2, V = 512 m 3

Question 17

An unusual architectural design requires triangular ducts that will be painted and exposed in the room. If the cross-sectional area is an equilateral triangle of 3.6 square feet, find the length of each side. Use the rules for working with measurements. Round to the nearest tenth, if necessary.

Accepted Answer

A)  2.9 ft 
B)  1.3 ft 
C)  6.2 ft 
D)  5.1 ft 
E)  1.8 ft 
A)  2.9 ft 
B)  1.3 ft 
C)  6.2 ft 
D)  5.1 ft 
E)  1.8 ft

Question 18

Find the length of the hypotenuse in the triangle. Use the rules for working with measurements.

Accepted Answer

A)  c = 49 m 
B)  c = 44 m 
C)  c = 40 m 
D)  c = 39 m 
E)  c = 41 m 
A)  c = 49 m 
B)  c = 44 m 
C)  c = 40 m 
D)  c = 39 m 
E)  c = 41 m

Question 19

Find the measure of $$\angle 1$$ in the illustration.

Accepted Answer

A)  ?1 = 90° 
B)  ?1 = 120° 
C)  ?1 = 30° 
D)  ?1 = 180° 
E)  ?1 = 60° 
A)  ?1 = 90° 
B)  ?1 = 120° 
C)  ?1 = 30° 
D)  ?1 = 180° 
E)  ?1 = 60°

Question 20

A round metal duct has a cross-section area of 134 square inches. What is the duct's diameter? Use the rules for working with measurements.

Accepted Answer

A)  The diameter is 10.3 in. 
B)  The diameter is 13.1 in. 
C)  The diameter is 26.1 in. 
D)  The diameter is 6.53 in. 
E)  The diameter is 52.2 in. 
A)  The diameter is 10.3 in. 
B)  The diameter is 13.1 in. 
C)  The diameter is 26.1 in. 
D)  The diameter is 6.53 in. 
E)  The diameter is 52.2 in.

Find the measure of the unknown angle.

Suppose l||m, $\angle 1 = 3 x - 50$ and $\angle 2 = x + 56$ . Find the value of x. $Suppose l||m, \angle 1 = 3 x - 50 and \angle 2 = x + 56 . Find the value of x.$

Follow the rules for working with measurements. Find the volume of the gravity bin shown in the illustration below.

Following the rules for working with measurements, find the area of the lateral surface to be painted in the illustration. Assume there are no windows.

Looking at the side of a welding metal storage bin, the shape is a trapezoid. The lengths of the bases are 58.8 cm and 62.0 cm, and the height is 48.8 cm. Find its area.

Follow the rules for working with measurements. A steel rod of a cross-sectional area 4 in. ² weighs 32 lb. Find its length. (Steel weighs 0.28 lb/in ³.)

Find the length of the hypotenuse in the triangle. Use the rules for working with measurements. c = __________ cm

Follow the rules for working with measurements. Find the volume of the figure. V = __________ in³.

Follow the rules for working with measurements. Find the volume of the figure.

Follow the rules for working with measurements. Find the volume and lateral surface area of the frustum of the cone shown in the illustration.

A plumber wishes to add a pipe parallel to an existing pipe as shown in the illustration. Find angle x.

An experimental balloon is to have a diameter of 5.68 m. How much material is needed for this balloon?

Follow the rules for working with measurements. A steel cylindrical tank must hold 8,500 gal of dyed water for a cloth process. Due to space constraints, the cylindrical tank is made 11 ft in diameter. How tall must the tank be? (Water weighs 8.34 lb/gal and 62.4 lb/ft ³.)

A plumber wishes to add a pipe parallel to an existing pipe as shown in illustration. Find angle x. $A plumber wishes to add a pipe parallel to an existing pipe as shown in illustration. Find angle x. ^ { \circ }$ $^ { \circ }$

Following the rules for working with measurements find the lateral surface area of the rectangular prism shown in the illustration above A _L, the total surface area of the prism A _T and the volume of the prism V.

An unusual architectural design requires triangular ducts that will be painted and exposed in the room. If the cross-sectional area is an equilateral triangle of 3.6 square feet, find the length of each side. Use the rules for working with measurements. Round to the nearest tenth, if necessary.

Find the length of the hypotenuse in the triangle. Use the rules for working with measurements.

Find the measure of $\angle 1$ in the illustration. $Find the measure of \angle 1 in the illustration.$

A round metal duct has a cross-section area of 134 square inches. What is the duct's diameter? 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

Find the measure of the unknown angle.

Suppose l||m, ∠1=3x−50\angle 1 = 3 x - 50∠1=3x−50 and ∠2=x+56\angle 2 = x + 56∠2=x+56 . Find the value of x.

Follow the rules for working with measurements. Find the volume of the gravity bin shown in the illustration below.

Following the rules for working with measurements, find the area of the lateral surface to be painted in the illustration. Assume there are no windows.

Looking at the side of a welding metal storage bin, the shape is a trapezoid. The lengths of the bases are 58.8 cm and 62.0 cm, and the height is 48.8 cm. Find its area.

Follow the rules for working with measurements. A steel rod of a cross-sectional area 4 in. 2 weighs 32 lb. Find its length. (Steel weighs 0.28 lb/in 3.)

Find the length of the hypotenuse in the triangle. Use the rules for working with measurements. c = __________ cm

Follow the rules for working with measurements. Find the volume of the figure. V = __________ in3.

Follow the rules for working with measurements. Find the volume of the figure.

Follow the rules for working with measurements. Find the volume and lateral surface area of the frustum of the cone shown in the illustration.

A plumber wishes to add a pipe parallel to an existing pipe as shown in the illustration. Find angle x.

An experimental balloon is to have a diameter of 5.68 m. How much material is needed for this balloon?

Follow the rules for working with measurements. A steel cylindrical tank must hold 8,500 gal of dyed water for a cloth process. Due to space constraints, the cylindrical tank is made 11 ft in diameter. How tall must the tank be? (Water weighs 8.34 lb/gal and 62.4 lb/ft 3.)

A plumber wishes to add a pipe parallel to an existing pipe as shown in illustration. Find angle x. __________ ∘^ { \circ }∘

Following the rules for working with measurements find the lateral surface area of the rectangular prism shown in the illustration above A L, the total surface area of the prism A T and the volume of the prism V.

An unusual architectural design requires triangular ducts that will be painted and exposed in the room. If the cross-sectional area is an equilateral triangle of 3.6 square feet, find the length of each side. Use the rules for working with measurements. Round to the nearest tenth, if necessary.

Find the length of the hypotenuse in the triangle. Use the rules for working with measurements.

Find the measure of ∠1\angle 1∠1 in the illustration.

A round metal duct has a cross-section area of 134 square inches. What is the duct's diameter? 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

Suppose l||m, $\angle 1 = 3 x - 50$ and $\angle 2 = x + 56$ . Find the value of x. $Suppose l||m, \angle 1 = 3 x - 50 and \angle 2 = x + 56 . Find the value of x.$

Follow the rules for working with measurements. A steel rod of a cross-sectional area 4 in. ² weighs 32 lb. Find its length. (Steel weighs 0.28 lb/in ³.)

Follow the rules for working with measurements. Find the volume of the figure. V = __________ in³.

Follow the rules for working with measurements. A steel cylindrical tank must hold 8,500 gal of dyed water for a cloth process. Due to space constraints, the cylindrical tank is made 11 ft in diameter. How tall must the tank be? (Water weighs 8.34 lb/gal and 62.4 lb/ft ³.)

A plumber wishes to add a pipe parallel to an existing pipe as shown in illustration. Find angle x. $A plumber wishes to add a pipe parallel to an existing pipe as shown in illustration. Find angle x. ^ { \circ }$ $^ { \circ }$

Following the rules for working with measurements find the lateral surface area of the rectangular prism shown in the illustration above A _L, the total surface area of the prism A _T and the volume of the prism V.

Find the measure of $\angle 1$ in the illustration. $Find the measure of \angle 1 in the illustration.$