Question 1

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.

Accepted Answer

The dimension of the object can be found using the formula for fractal dimension, $D = \frac{\log(N)}{\log(S)}$, where $N$ is the factor by which the number of length elements increases, and $S$ is the scale factor by which the length is reduced. Here, $N = 12$ and $S = 3$, so $D = \frac{\log(12)}{\log(3)} = 2.262$. Since the dimension is not an integer and greater than 1, the object is a fractal.

Question 2

Convert the given angle measure into degrees and decimal fractions of a degree.
-$78 ^ { \circ } 57 ^ { \prime }$

Accepted Answer

The answer of Convert the given angle measure into degrees...

Question 3

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?

Accepted Answer

The answer of Use the formula relating angular size, physical...

Question 4

Solve the problem.
-A toy ball has a diameter of $4.44$ inches. What are its volume and surface area?

Accepted Answer

The volume of a sphere is $(4/3)\pi r^3$ and the surface area is $4\pi r^2$. So, the volume is $(4/3)\pi (2.22)^3 = 45.8$ in. $^ { 3 }$ and the surface area is $4\pi (2.22)^2 = 61.9$ in. $^ { 2 }$.

Question 5

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

The volume of the pool is calculated by multiplying its length, width, and depth: $25 \times 21 \times 3 = 1575 \mathrm {~m} ^ { 3 }$.

Question 6

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?

Accepted Answer

Steve's waist is also 21% larger than Andy's. So, Steve's waist = 44 inches * 1.21 = 53.24 inches, rounded to 53 inches.

Question 7

Convert the given angle measure into degrees and decimal fractions of a degree.
-247°35'1"

Accepted Answer

To convert 247°35'1" into decimal degrees, convert the minutes and seconds into a fraction of a degree: 35' = 35/60 degrees and 1" = 1/3600 degrees. Adding these to 247 gives 247 + 35/60 + 1/3600 = 247.584 degrees.

Question 8

Find the degree measure of the angle created by the given part of a circle.
-$\frac { 1 } { 4 }$ circle

Accepted Answer

A full circle is $360^\circ$, so a quarter of a circle ($\frac{1}{4}$) would be $360^\circ \times \frac{1}{4} = 90^\circ$.

Question 9

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

Accepted Answer

For the circular enclosure, the perimeter (circumference) is given as $107 \mathrm{m}$. The formula for the circumference of a circle is $C = 2\pi r$, where $r$ is the radius. Solving for $r$ gives $r = \frac{107}{2\pi}$. The area of a circle is $A = \pi r^2$, substituting $r$ gives $A = \pi \left(\frac{107}{2\pi}\right)^2 \approx 911 \mathrm{m}^2$. For the square enclosure, the perimeter is $107 \mathrm{m}$, and since a square has four equal sides, each side is $\frac{107}{4} = 26.75 \mathrm{m}$. The area of a square is $side^2$, so $26.75^2 = 716 \mathrm{m}^2$.

Question 10

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?

Accepted Answer

The answer of Use the formula relating angular size, physical...

Question 11

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.

Accepted Answer

To find the area in acres, multiply the stream frontage by the property line and divide by 43,560 (the number of square feet in an acre): (791 * 2120) / 43,560 = 17.86 acres.

Question 12

Provide an appropriate response.
-The word geometry means __________.

Accepted Answer

The word "geometry" originates from the Greek words "geo," meaning earth, and "metron," meaning measure, thus it translates to "earth measure."

Question 13

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

Accepted Answer

This is a statement of the Pythagorean theorem, which applies to right triangles.

Question 14

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?

Accepted Answer

The surface area of similar shapes is proportional to the square of the scale factor. Since the scale factor is 39, the surface area of the actual concert hall will be $39^2 = 1521$ times as great as the surface area of the scale model.

Question 15

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?

Accepted Answer

The answer of Use the formula relating angular size, physical...

Question 16

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

The answer of Solve.
-A 15-foot fence on the property line...

Question 17

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

Accepted Answer

The circumference of a circle is given by the formula C = 2πr, where r is the radius. For a radius of 10.5 yards, the circumference is C = 2 * π * 10.5 ≈ 65.97 yards, which rounds to 65.9 yards.

Question 18

Determine if the pair of triangles are similar.
-

Accepted Answer

The answer of Determine if the pair of triangles are...

Question 19

Provide an appropriate response.
-What is the slope of a 2 in 14 roof?

Accepted Answer

The slope of a roof is calculated by dividing the rise by the run. For a 2 in 14 roof, the rise is 2 and the run is 14, so the slope is $\frac{2}{14} = \frac{1}{7} = 0.14$.

Question 20

Provide an appropriate response.
-A geometric line is formed by the shortest path between any 2 points.

Accepted Answer

A geometric line, by definition, represents the shortest distance between any two points, extending infinitely in both directions.

Quiz 10: Modeling With Geometry

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.

Convert the given angle measure into degrees and decimal fractions of a degree. - $78 ^ { \circ } 57 ^ { \prime }$

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?

Solve the problem. -A toy ball has a diameter of $4.44$ inches. What are its volume and surface area?

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?

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?

Convert the given angle measure into degrees and decimal fractions of a degree. -247°35'1"

Find the degree measure of the angle created by the given part of a circle. - $\frac { 1 } { 4 }$ circle

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

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?

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.

Provide an appropriate response. -The word geometry means __________.

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

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?

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?

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.

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

Determine if the pair of triangles are similar. -

Provide an appropriate response. -What is the slope of a 2 in 14 roof?

Provide an appropriate response. -A geometric line is formed by the shortest path between any 2 points.

Quiz 10: Modeling With Geometry

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.

Convert the given angle measure into degrees and decimal fractions of a degree. - 78∘57′78 ^ { \circ } 57 ^ { \prime }78∘57′

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?

Solve the problem. -A toy ball has a diameter of 4.444.444.44 inches. What are its volume and surface area?

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?

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?

Convert the given angle measure into degrees and decimal fractions of a degree. -247°35'1"

Find the degree measure of the angle created by the given part of a circle. - 14\frac { 1 } { 4 }41​ circle

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

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?

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.

Provide an appropriate response. -The word geometry means __________.

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

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?

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?

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.

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

Determine if the pair of triangles are similar. -

Provide an appropriate response. -What is the slope of a 2 in 14 roof?

Provide an appropriate response. -A geometric line is formed by the shortest path between any 2 points.

Convert the given angle measure into degrees and decimal fractions of a degree. - $78 ^ { \circ } 57 ^ { \prime }$

Solve the problem. -A toy ball has a diameter of $4.44$ inches. What are its volume and surface area?

Find the degree measure of the angle created by the given part of a circle. - $\frac { 1 } { 4 }$ circle