Question 1

Solve.
-Determine the area of a circular enclosure and a square enclosure made with 721 feet of fence. Use $\pi = 3.1416$

Accepted Answer

A)  Circular: $41,368 \mathrm { ft } ^ { 2 }$; square: $32,490 \mathrm { ft } ^ { 2 }$ 
B)  Circular: 28,200 ft ; square: $32,490 \mathrm { ft } ^ { 2 }$ 
C)  Circular: 28,200 ft 2 ; square: $129,960 \mathrm { ft } ^ { 2 }$ 
D)  Circular: $41,368 \mathrm { ft } ^ { 2 }$; square: $129,960 \mathrm { ft } ^ { 2 }$ 
A)  Circular: $41,368 \mathrm { ft } ^ { 2 }$; square: $32,490 \mathrm { ft } ^ { 2 }$ 
B)  Circular: 28,200 ft ; square: $32,490 \mathrm { ft } ^ { 2 }$ 
C)  Circular: 28,200 ft 2 ; square: $129,960 \mathrm { ft } ^ { 2 }$ 
D)  Circular: $41,368 \mathrm { ft } ^ { 2 }$; square: $129,960 \mathrm { ft } ^ { 2 }$

Question 2

Find the degree measure of the angle created by the given part of a circle.
-$\frac { 4 } { 5 }$ circle

Accepted Answer

A)  $288 ^ { \circ }$ 
B)  $180 ^ { \circ }$ 
C)  $144 ^ { \circ }$ 
D)  $90 ^ { \circ }$ 
A)  $288 ^ { \circ }$ 
B)  $180 ^ { \circ }$ 
C)  $144 ^ { \circ }$ 
D)  $90 ^ { \circ }$

Question 3

Convert the given degree measure into degrees, minutes, and seconds of arc.
-$73.72 ^ { \circ }$

Accepted Answer

A)  $73 ^ { \circ } 43 ^ { \prime } 0 ^ { \prime \prime }$ 
B)  $73 ^ { \circ } 43 ^ { \prime } 72 ^ { \prime \prime }$ 
C)  $73 ^ { \circ } 43 ^ { \prime } 12 ^ { \prime \prime }$ 
D)  $73 ^ { \circ } 43 ^ { \prime } 18 ^ { \prime \prime }$ 
A)  $73 ^ { \circ } 43 ^ { \prime } 0 ^ { \prime \prime }$ 
B)  $73 ^ { \circ } 43 ^ { \prime } 72 ^ { \prime \prime }$ 
C)  $73 ^ { \circ } 43 ^ { \prime } 12 ^ { \prime \prime }$ 
D)  $73 ^ { \circ } 43 ^ { \prime } 18 ^ { \prime \prime }$

Question 4

Provide an appropriate response.
-Define a fractal object.

Accepted Answer

A) An object that can be magnified. 
B) An object that reveals new features at smaller scales. 
C) An object with several edges that can be revealed at larger scales. 
D) An object with many jagged edges. 
A) An object that can be magnified. 
B) An object that reveals new features at smaller scales. 
C) An object with several edges that can be revealed at larger scales. 
D) An object with many jagged edges.

Question 5

Convert the given degree measure into degrees, minutes, and seconds of arc.
-$180.19 ^ { \circ }$

Accepted Answer

A)  $180 ^ { \circ } 9 ^ { \prime } 19 ^ { \prime \prime }$ 
B)  $180 ^ { \circ } 11 ^ { \prime } 19 ^ { \prime \prime }$ 
C)  $180 ^ { \circ } 12 ^ { \prime } 24 ^ { \prime \prime }$ 
D)  $180 ^ { \circ } 11 ^ { \prime } 24 ^ { \prime \prime }$ 
A)  $180 ^ { \circ } 9 ^ { \prime } 19 ^ { \prime \prime }$ 
B)  $180 ^ { \circ } 11 ^ { \prime } 19 ^ { \prime \prime }$ 
C)  $180 ^ { \circ } 12 ^ { \prime } 24 ^ { \prime \prime }$ 
D)  $180 ^ { \circ } 11 ^ { \prime } 24 ^ { \prime \prime }$

Question 6

Provide an appropriate response.
-In Euclidean geometry, a triangle with two acute angles and one obtuse angle is impossible to construct.

Accepted Answer

A) True 
 B)False

Question 7

Solve.
-A 15-foot fence on the property line would cast a 50-foot shadow on the shortest day of the year, and the north side of the apartment building is set back 60 feet from the property line. Find the
Maximum allowed height of the apartment building.

Accepted Answer

A) 30.8 ft 
B) 18 ft 
C) 28.6 ft 
D) 33 ft 
A) 30.8 ft 
B) 18 ft 
C) 28.6 ft 
D) 33 ft

Question 8

Find the dimension of the object and state whether or not it is a fractal.
-In measuring the length of the object, when you reduce the length of your ruler by a factor of 6, the number of length elements increases by a factor of 7.

Accepted Answer

A) The dimension is 2.086 and the object is fractal. 
B) The dimension is 1 and the object is ordinary (non-fractal). 
C) The dimension is 1.086 and the object is fractal. 
D) The dimension is 0.921 and the object is fractal. 
A) The dimension is 2.086 and the object is fractal. 
B) The dimension is 1 and the object is ordinary (non-fractal). 
C) The dimension is 1.086 and the object is fractal. 
D) The dimension is 0.921 and the object is fractal.

Question 9

Solve the problem.
-A competition swimming pool is 25 meters long, 21 meters wide, and 3 meters deep. How much water does the pool hold?

Accepted Answer

A)  $225 \mathrm {~m} ^ { 3 }$ 
B)  $11,025 \mathrm {~m} ^ { 3 }$ 
C)  $13,125 \mathrm {~m} ^ { 3 }$ 
D)  $1575 \mathrm {~m} ^ { 3 }$ 
A)  $225 \mathrm {~m} ^ { 3 }$ 
B)  $11,025 \mathrm {~m} ^ { 3 }$ 
C)  $13,125 \mathrm {~m} ^ { 3 }$ 
D)  $1575 \mathrm {~m} ^ { 3 }$

Question 10

Provide an appropriate response.
-If a roof with a pitch of 3 in 15 rises in the horizontal direction for 3.4 feet, how high is it vertically?

Accepted Answer

A) 2.83 ft 
B) 0.57 ft 
C) 3.4 ft 
D) 17 ft 
A) 2.83 ft 
B) 0.57 ft 
C) 3.4 ft 
D) 17 ft

Question 11

Solve the problem.
-Suppose you build an architectural model of a new office complex using a scale factor of 74. How will the height of the actual office complex compare to the height of the scale model?

Accepted Answer

A) 37 times as great 
B) 5476 times as great 
C) 148 times as great 
D) 74 times as great 
A) 37 times as great 
B) 5476 times as great 
C) 148 times as great 
D) 74 times as great

Question 12

Solve the problem.
-If you magically quadrupled in size, how much more material will be required for your new set of clothes?

Accepted Answer

A) 4 
B) 3 
C) 16 
D) 64 
A) 4 
B) 3 
C) 16 
D) 64

Question 13

Provide an appropriate response.
-To create the Snowflake curve, the first step is to .

Accepted Answer

A) use a smaller ruler 
B) divide the line segment into three equal pieces 
C) divide the line segment in half 
D) find the fractal dimension 
A) use a smaller ruler 
B) divide the line segment into three equal pieces 
C) divide the line segment in half 
D) find the fractal dimension

Question 14

Provide an appropriate response.
-A cube is an example of a solid.

Accepted Answer

A) True 
 B)False

Question 15

Find the perimeter and area of the figure.
-A square with sides of length $6.9$ yards

Accepted Answer

A)  $\mathrm { P } = 13.8 \mathrm { yd } , \mathrm { A } = 95.22 \mathrm { yd } 2$ 
B)  $P = 27.6 \mathrm { yd } , \mathrm { A } = 47.61 \mathrm { yd } ^ { 2 }$ 
C)  $P = 95.22 \mathrm { yd } , \mathrm { A } = 47.61 \mathrm { yd } ^ { 2 }$ 
D)  $P = 37.6 \mathrm { yd } , \mathrm { A } = 95.22 \mathrm { yd } ^ { 2 }$ 
A)  $\mathrm { P } = 13.8 \mathrm { yd } , \mathrm { A } = 95.22 \mathrm { yd } 2$ 
B)  $P = 27.6 \mathrm { yd } , \mathrm { A } = 47.61 \mathrm { yd } ^ { 2 }$ 
C)  $P = 95.22 \mathrm { yd } , \mathrm { A } = 47.61 \mathrm { yd } ^ { 2 }$ 
D)  $P = 37.6 \mathrm { yd } , \mathrm { A } = 95.22 \mathrm { yd } ^ { 2 }$

Question 16

Determine if the pair of triangles are similar.
-

Accepted Answer

A) Not similar 
B) Similar 
A) Not similar 
B) Similar

Question 17

The two triangles below are similar. Find the missing lengths.
-

Accepted Answer

A)  $x = 23$ 
B)  $x = 16$ 
C)  $x = 24$ 
D)  $x = 30$ 
A)  $x = 23$ 
B)  $x = 16$ 
C)  $x = 24$ 
D)  $x = 30$

Question 18

Find the dimension of the object and state whether or not it is a fractal.
-In measuring the volume of the object, when you reduce the length of your ruler by a factor of 5, the number of length elements increases by a factor of 60.

Accepted Answer

A) The dimension is 55 and the object is ordinary (non-fractal). 
B) The dimension is 2.544 and the object is fractal. 
C) The dimension is 0.393 and the object is fractal. 
D) The dimension is 3.544 and the object is fractal. 
A) The dimension is 55 and the object is ordinary (non-fractal). 
B) The dimension is 2.544 and the object is fractal. 
C) The dimension is 0.393 and the object is fractal. 
D) The dimension is 3.544 and the object is fractal.

Question 19

Find the fraction of a circle that encloses the given angle.
-270°

Accepted Answer

A)  $\frac { 1 } { 18 }$ 
B)  $\frac { 3 } { 4 }$ 
C)  $\frac { 1 } { 17 }$ 
D)  $\frac { 1 } { 9 }$ 
A)  $\frac { 1 } { 18 }$ 
B)  $\frac { 3 } { 4 }$ 
C)  $\frac { 1 } { 17 }$ 
D)  $\frac { 1 } { 9 }$

Question 20

Provide an appropriate response.
-How long is the perimeter of a snowflake island?

Accepted Answer

A) it is infinite 
B) it is the same as the area 
C) 3 times the height 
D) 2 times the height 
A) it is infinite 
B) it is the same as the area 
C) 3 times the height 
D) 2 times the height

Solve. -Determine the area of a circular enclosure and a square enclosure made with 721 feet of fence. Use $\pi = 3.1416$

Find the degree measure of the angle created by the given part of a circle. - $\frac { 4 } { 5 }$ circle

Convert the given degree measure into degrees, minutes, and seconds of arc. - $73.72 ^ { \circ }$

Provide an appropriate response. -Define a fractal object.

Convert the given degree measure into degrees, minutes, and seconds of arc. - $180.19 ^ { \circ }$

Provide an appropriate response. -In Euclidean geometry, a triangle with two acute angles and one obtuse angle is impossible to construct.

Solve. -A 15-foot fence on the property line would cast a 50-foot shadow on the shortest day of the year, and the north side of the apartment building is set back 60 feet from the property line. Find the Maximum allowed height of the apartment building.

Find the dimension of the object and state whether or not it is a fractal. -In measuring the length of the object, when you reduce the length of your ruler by a factor of 6, the number of length elements increases by a factor of 7.

Solve the problem. -A competition swimming pool is 25 meters long, 21 meters wide, and 3 meters deep. How much water does the pool hold?

Provide an appropriate response. -If a roof with a pitch of 3 in 15 rises in the horizontal direction for 3.4 feet, how high is it vertically?

Solve the problem. -Suppose you build an architectural model of a new office complex using a scale factor of 74. How will the height of the actual office complex compare to the height of the scale model?

Solve the problem. -If you magically quadrupled in size, how much more material will be required for your new set of clothes?

Provide an appropriate response. -To create the Snowflake curve, the first step is to .

Provide an appropriate response. -A cube is an example of a solid.

Find the perimeter and area of the figure. -A square with sides of length $6.9$ yards

Determine if the pair of triangles are similar. -

The two triangles below are similar. Find the missing lengths. -

Find the dimension of the object and state whether or not it is a fractal. -In measuring the volume of the object, when you reduce the length of your ruler by a factor of 5, the number of length elements increases by a factor of 60.

Find the fraction of a circle that encloses the given angle. -270°

Provide an appropriate response. -How long is the perimeter of a snowflake island?

Thinking Critically

Approaches to Problem Solving

Numbers in the Real World

Managing Money

Statistical Reasoning

Putting Statistics to Work

Probability: Living With the Odds

Exponential Astonishment

Modeling Our World

Mathematics and the Arts

Filters

Exam 10: Modeling With Geometry

Solve. -Determine the area of a circular enclosure and a square enclosure made with 721 feet of fence. Use π=3.1416\pi = 3.1416π=3.1416

Find the degree measure of the angle created by the given part of a circle. - 45\frac { 4 } { 5 }54​ circle

Convert the given degree measure into degrees, minutes, and seconds of arc. - 73.72∘73.72 ^ { \circ }73.72∘