Deck 10: Modeling With Geometry

Question 1

Provide an appropriate response.
In fractal geometry, the perimeter of a region is and the area is .

A)unlimited; unlimited
B)limited; unlimited
C)unlimited; limited
D)limited; limited

Answer 1

C

Question 2

Provide an appropriate response.
What mathematical tool is helpful in finding the fractal dimension?

A)iteration
B)integration
C)tangent
D)logarithm

Answer 2

D

Question 3

Provide an appropriate response.
Define a self-similar fractal.

A)can be created by finding the fractal dimension
B)has a fractal dimension greater than 2
C)looks similar to itself when examined at different scales
D)has a fractal dimension between 0 and 1

Answer 3

C

Question 4

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

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 5

Provide an appropriate response.
The Sierpinski sponge has a fractal dimension between .

A)1 and 2
B)3 and 4
C)0 and 1
D)2 and 3

Question 6

Provide an appropriate response.
In fractal geometry, the shorter the ruler .

A)the less accurate the measurement
B)the longer the perimeter
C)the more accurate the measurement
D)the shorter the perimeter

Question 7

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

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

Question 8

Find the area of the triangle.

Question 9

Solve. Round your answer to the nearest tenth.
Find the circumference of a circle with a diameter of 32 feet.

A)50.2 ft
B)803.8 ft
C)100.5 ft
D)201.0 ft

Question 10

Find the perimeter and area of the figure.
A square with sides of length 3.9 feet

Question 11

Provide an appropriate response.
Define a random iteration.

A)an iteration that is self-similar.
B)an iteration with slight variations in every iteration.
C)an iteration that doesn't produce a fractal.

Question 12

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

Question 13

Provide an appropriate response.
To create a Sierpinski triangle, start with a solid black triangle and iterate what rules?

A)Connect the endpoints of the sides and inserting an isosceles triangle.
B)Draw an isosceles triangle extending from each side.
C)Connect the midpoints of the sides and remove the resulting inner triangle.
D)Delete the middle third of each line segment of the triangle.

Question 14

Provide an appropriate response.
Solving for fractal dimension, we use the rule that .

Question 15

Provide an appropriate response.
Define a fractal object.

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 16

Solve the problem.
If you magically quadrupled in size, by what factor has your waist size increased?

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

Question 17

Provide an appropriate response.
The fractal dimension of a coastline .

A)is less than 1
B)is between 1 and 2
C)is between 0 and 1
D)is greater than 2

Question 18

Provide an appropriate response.
The process of repeating a rule over and over to generate a self-similar fractal is called .

A)interpretation
B)iteration
C)fractalization
D)repetition

Question 19

Determine if the pair of triangles are similar.

A)Not similar
B)Similar

Question 20

Provide an appropriate response.
True or False? Two triangles are similar if they have the same size, but not necessarily the same
shape.

Question 21

Find the degree measure of the angle created by the given part of a circle.

A)24°
B)6°
C)12°
D)3°

Question 22

Find the area of the triangle.

Question 23

Find the perimeter.

Question 24

Solve the problem.
A semi-circular transom above a door is to contain a stained glass window. If the stained glass window costs $1.40 per square inch, how much will the window cost?

Question 25

Solve the problem.
Suppose you build an architectural model of a new concert hall using a scale factor of 34. How will the volume of the actual concert hall compare to the volume of the square model?

A)34 times as great
B)39,304 times as great
C)1156 times as great
D)102 times as great

Question 26

Use the formula relating angular size, physical size and distance.
A planet has an angular diameter of about 1° and a distance of about 88 million kilometers. What is its true diameter?

A)1.54 million kilometers
B)10.34 million kilometers
C)11.87 million kilometers
D)3.07 million kilometers

Question 27

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

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

Question 28

Find the fraction of a circle that encloses the given angle.

Question 29

Solve.
Determine the area of a circular enclosure and a square enclosure made with 721 feet of fence. Use

Question 30

Solve.
Suppose you are designing a cardboard box that must have a volume of 18 cubic feet. The cost of the cardboard is $6 per square foot. How much will the material for each box cost?

A)$247.26
B)$123.63
C)$329.68
D)$164.84

Question 31

Provide an appropriate response.

Question 32

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 3 the number of length elements increases by a factor of 27.

A)The dimension is 1 and the object is ordinary (non-fractal).
B)The dimension is 2 and the object is ordinary (non-fractal).
C)The dimension is 3 and the object is a fractal.
D)The dimension is 3 and the object is ordinary (non-fractal).

Question 33

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?

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

Question 34

Solve.
Determine the area of a circular enclosure and a square enclosure made with 1495 yards of fence. Use

Question 35

Convert the given angle measure into degrees and decimal fractions of a degree.

Question 36

Solve. Round your answer to the nearest tenth.
Find the circumference of a circle with a diameter of 13 feet.

A)81.6 ft
B)40.8 ft
C)132.7 ft
D)20.4 ft

Question 37

Find the degree measure of the angle created by the given part of a circle.

Question 38

Convert the given degree measure into degrees, minutes, and seconds of arc.

Question 39

Provide an appropriate response.
True or False? A cube is an example of a solid.

A)False
B)True

Question 40

Convert the given degree measure into degrees, minutes, and seconds of arc.

Question 41

Find the perimeter and area of the figure.
A parallelogram with sides of length of 4.5 feet and 9 feet, and a distance between the 9-foot sides of 0.8 foot.

Question 42

Provide an appropriate response.
What is the approximate grade of a path that rises 891 feet every mile?

A)1.01%
B)0.51%
C)16.88%
D)13.5%

Question 43

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

A)False
B)True

Question 44

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?

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

Question 45

Solve the problem.
City A is nearly at the same longitude as City B, but City A's latitude is 52°N while City B's latitude is 17°N. About how far away is City A from City B?

A)3500 mi
B)4830 mi
C)2450 mi
D)6900 mi

Question 46

Provide an appropriate response.
How much does a road with a 27% grade rise for each horizontal foot?

A)0.27 ft
B)0.243 ft
C)0.216 ft
D)0.297 ft

Question 47

Solve the problem.
Find the area of the skating rink. Round to the nearest tenth.

Question 48

Solve the problem.
Steve is 11% taller than Andy but proportioned in exactly the same way. If Andy is 75 inches tall, how tall is Steve?

A)91 in.
B)80 in.
C)87 in.
D)83 in.

Question 49

Provide an appropriate response.
True or False? Longitude measures positions east or west position.

A)False
B)True

Question 50

Refer to the given map. Assume that the length of each east-west block is mile and the length of each north-southblock is mile.
Find the straight-line distance between the bus stop and the theater.

A)1.27 mi
B)1.58 mi
C)1.33 mi
D)1.50 mi

Question 51

Refer to the given map. Assume that the length of each east-west block is mile and the length of each north-southblock is mile.
Find the straight-line distance between the bus stop and the grocery store.

A)0.96 mi
B)1.22 mi
C)1.06 mi
D)1.43 mi

Question 52

Solve the problem.
If you magically doubled in size, by what factor has your weight increased?

A)8
B)4
C)1
D)2

Question 53

Provide an appropriate response.
How many dimensions does a plane have?

A)0
B)1
C)3
D)2

Question 54

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

Question 55

Find the perimeter and area of the figure.
A square with sides of length 4.9 feet

Question 56

Refer to the given map. Assume that the length of each east-west block is mile and the length of each north-southblock is mile.
Find the straight-line distance between the grocery store and the library.

A)0.75 mi
B)0.63 mi
C)0.48 mi
D)0.56 mi

Question 57

Find the perimeter.

Question 58

Provide an appropriate response.
How many dimensions does a point have?

A)0
B)3
C)1
D)2

Question 59

Provide an appropriate response.
Who was the first mathematician to summarize many of the ideas of geometry?

A)Euclid
B)Pascal
C)Pythagoras
D)Newton

Question 60

Solve. Round your answer to the nearest tenth.
Find the area of a circle with a diameter of 38 feet.

Question 61

Find the dimension of the object and state whether or not it is a fractal.
In measuring the area of the object, when you reduce the length of your ruler by a factor of 3, the number of length elements increases by a factor of 12.

A)The dimension is 0.442 and the object is fractal.
B)The dimension is 9 and the object is ordinary (non-fractal).
C)The dimension is 2.262 and the object is fractal.
D)The dimension is 3.262 and the object is fractal.

Question 62

Convert the given angle measure into degrees and decimal fractions of a degree.

Question 63

Use the formula relating angular size, physical size and distance.
What is the angular size of a quarter viewed from a distance of 20 yards?

A)2.86°
B)4.2°
C)0.17°
D)0.08°

Question 64

Solve the problem.

Question 65

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?

Question 66

Solve the problem.
Steve is 21% taller than Andy but proportioned in exactly the same way. If Andy's waist is 44 inches, what is Steve's waist?

A)58 in.
B)53 in.
C)55 in.
D)51 in.

Question 67

Convert the given angle measure into degrees and decimal fractions of a degree.

Question 68

Find the degree measure of the angle created by the given part of a circle.

Question 69

Solve.
Determine the area of a circular enclosure and a square enclosure made with 107 meters of fence.

Question 70

Use the formula relating angular size, physical size and distance.
A planet has an angular diameter of about 0.9° and a distance of about 135 million kilometers. What is its true diameter?

A)14.27 million kilometers
B)16.39 million kilometers
C)2.12 million kilometers
D)4.24 million kilometers

Question 71

Find the area in acres of the property under the given assumptions. Refer to the figure.
The stream frontage is 791 feet in length and the property line is 2120 feet in length.

A)8.93 acre
B)35.72 acre
C)17.86 acre
D)26.79 acre

Question 72

Provide an appropriate response.
The word geometry means __________.

A)triangle forming
B)earth measure
C)shape measure
D)mountain shape

Question 73

Provide an appropriate response.
In a right triangle, the square of the length of the hypotenuse is equal to the ________.

A)sum of the squares of the other two sides
B)square root of the sum of the other two side
C)area of the triangle
D)sum of the lengths of the other two sides

Question 74

Solve the problem.
Suppose you build an architectural model of a new concert hall using a scale factor of 39. How will the surface area of the actual concert hall compare to the surface area of the scale model?

A)39 times as great
B)1521 times as great
C)78 times as great
D)59,319 times as great

Question 75

Use the formula relating angular size, physical size and distance.
What is the angular size of a quarter viewed from a distance of 73 yards?

A)0.05°
B)1.15°
C)0.02°
D)0.78°

Question 76

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.

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

Question 77

Solve. Round your answer to the nearest tenth.
Find the circumference of a circle with a radius of 10.5 yards.

A)65.9 yd
B)33.0 yd
C)346.2 yd
D)13.3 yd

Question 78

Determine if the pair of triangles are similar.

A)Not similar
B)Similar

Question 79

Provide an appropriate response.

Question 80

Provide an appropriate response.
True or False? A geometric line is formed by the shortest path between any 2 points.

A)False
B)True