Question 1

Draw a rectangular region on your paper that covers an estimated actual area of 8 square centimeters.

Accepted Answer

Check for something in the neighborhood of 8 square centimeters, unless you allowed a ruler.

Question 2

Find the area of the trapezoid below using (A) the triangular region below as the unit of measurement and (B) the square region below as the unit of measurement:

Accepted Answer

A) 6
B) 12

Question 3

A) Find the area of the polygonal region on the geoboard. (Use the natural unit.)

B) Which key idea(s) of measurement did you use in part A?

Accepted Answer

A) 17 $\frac { 1 } { 2 }$ square units
B) The whole 5-by-6 rectangle can be measured by adding the areas of its parts, and the target region is one of them: 2 + 3 + 2 + 1 $\frac { 1 } { 2 }$ + 1 + 3 + A = 5 × 6 = 30, or 12 $\frac { 1 } { 2 }$ + A = 30.

Question 4

Explain how could you illustrate to a child that there are 1,000,000 cubic centimeters in a cubic meter.

Accepted Answer

The answer of Explain how could you illustrate to a...

Question 5

If one cube has an edge of 2 centimeters and another has an edge of 3 centimeters, then the ratio of their volumes is _____.

Accepted Answer

The answer of If one cube has an edge of...

Question 6

Give the surface area and the volume of each three-dimensional shape shown. Use the natural units. (Note to the instructor: You may wish to choose just one of the shapes.)

Accepted Answer

The answer of Give the surface area and the volume...

Question 7

Seven cubic meters have the same volume as _____ cubic decimeters.

Accepted Answer

The answer of Seven cubic meters have the same volume...

Question 8

Complete the following, using your "metric sense" as much as possible. 
A) $2.7\mathrm {~kg} =$$\underline{\quad\quad}$$g$
B) $15.3 \mathrm {~m} = \quad \underline{\quad\quad}\mathrm { cm }$
C) $12 \mathrm {~mm} =$ $\underline{\quad\quad} \mathrm { cm }$ 
D) $2153 \mathrm {~g} = \quad \mathrm { \underline{\quad\quad}kg }$
E) $2.3 \mathrm {\underline{\quad\quad} mm} ^ { 2 } = \quad \mathrm { cm } ^ { 2 }$ 
F) $0.4 \mathrm {m} ^ { 2 } = \quad\underline{\quad\quad}\mathrm { cm } ^ { 2 }$
G) $ 2257 \mathrm{~cm}^{3}= $ $ \underline{\quad\quad}\mathrm{dm}^{3} $ 
H) $0.4 \mathrm {~m} ^ { 3 } = \quad\underline{\quad\quad}  \mathrm { cm } ^ { 3 }$
I) $232 \mathrm {~m} ^ { 3 } =$$\underline{\quad\quad}$  L
J) $300 \mathrm {~mL} =$$ \underline{\quad\quad}$$\mathrm { cm } ^ { 3 }$

Accepted Answer

A) 2700
B) 1530
C) 1

Question 9

There are _____ square decimeters in 9 square centimeters.

Accepted Answer

The answer of There are _____ square decimeters in 9...

Question 10

A child says, "I don't get it! One 1 equals 3 feet, right? So why don't 2 square yards equal 6 square feet?" What would you say to this child to help him or her understand? (Feel free to draw pictures if that would be helpful.)

Accepted Answer

The answer of A child says, "I don't get it!...

Question 11

Cube A has edges that are three times as long as the edges of cube B. The volume of cube A is 108 cubic centimeters. What is the volume of cube B?

Accepted Answer

A)  36 cubic centimeters 
B)  324 cubic centimeters 
C)  12 cubic centimeters 
D)  4 cubic centimeters 
E)  None of the answers is correct. 
A)  36 cubic centimeters 
B)  324 cubic centimeters 
C)  12 cubic centimeters 
D)  4 cubic centimeters 
E)  None of the answers is correct.

Question 12

Four gallons of paint were required to paint a scale model of a jet. The actual jet required 100 gallons of paint to be painted. What scale factor is associated with changing all of the length dimensions of the actual jet?

Accepted Answer

@#LAT-DLM& (Even though the pa

Question 13

A right rectangular prism, which is 3 centimeters by 5 centimeters by 2 centimeters in size, is similar to a larger shape with a scale factor of 2. What is the total surface area of the larger shape?

Accepted Answer

A)  60 square centimeters 
B)  120 square centimeters 
C)  124 square centimeters 
D)  248 square centimeters 
E)  None of the answers is correct. 
A)  60 square centimeters 
B)  120 square centimeters 
C)  124 square centimeters 
D)  248 square centimeters 
E)  None of the answers is correct.

Question 14

Find the exact area of the figures below. 
A)

B)

Accepted Answer

A) 6 @#LAT-DLM&  squ

Question 15

Ollie measures the area of his kitchen floor and finds that it is 2400 square decimeters. He needs to know how many square meters it is. Please help him by answering the question, and explain your response so that it will make sense to him. A diagram may be helpful.

Accepted Answer

The answer of Ollie measures the area of his kitchen...

Question 16

What is the area of the figure below? (Use the natural unit.)

Accepted Answer

A)  35 square units 
B)  30 square units 
C)  30$\frac { 1 } { 2 }$ square units 
D)  32 square units 
E)  None of the answers is correct. 
A)  35 square units 
B)  30 square units 
C)  30$\frac { 1 } { 2 }$ square units 
D)  32 square units 
E)  None of the answers is correct.

Question 17

Bill used 8 gallons of paint to paint a reduced model of his airplane. His actual airplane is similar to the model, but five times as long. How many gallons of paint will Fred need to paint his actual airplane? (Hint: What characteristic is involved in painting the surface of a jet?)

Accepted Answer

The answer of Bill used 8 gallons of paint to...

Question 18

State an appropriate unit of measurement for the following.
A) the width of an airplane runway
B) the amount of water in a bathtub
C) the area covered by a painting
D) the arc that the tip of a clock hand traces out as it moves from one number to the next

Accepted Answer

The answer of State an appropriate unit of measurement for...

Question 19

What is the area in square centimeters of the right triangle given below?

Accepted Answer

A)  60 square centimeters 
B)  120 square centimeters 
C)  240 square centimeters 
D)  260 square centimeters 
E)  None of these answers is correct. 
A)  60 square centimeters 
B)  120 square centimeters 
C)  240 square centimeters 
D)  260 square centimeters 
E)  None of these answers is correct.

Question 20

How is area different from volume? Can anything have area without having volume? Can anything have volume without having area? Give an example.

Accepted Answer

The answer of How is area different from volume? Can...

Exam 24: Area, Surface Area, and Volume

Draw a rectangular region on your paper that covers an estimated actual area of 8 square centimeters.

Find the area of the trapezoid below using (A) the triangular region below as the unit of measurement and (B) the square region below as the unit of measurement:

A) Find the area of the polygonal region on the geoboard. (Use the natural unit.) B) Which key idea(s) of measurement did you use in part A?

Explain how could you illustrate to a child that there are 1,000,000 cubic centimeters in a cubic meter.

If one cube has an edge of 2 centimeters and another has an edge of 3 centimeters, then the ratio of their volumes is _____.

Give the surface area and the volume of each three-dimensional shape shown. Use the natural units. (Note to the instructor: You may wish to choose just one of the shapes.)

Seven cubic meters have the same volume as _____ cubic decimeters.

There are _____ square decimeters in 9 square centimeters.

A child says, "I don't get it! One 1 equals 3 feet, right? So why don't 2 square yards equal 6 square feet?" What would you say to this child to help him or her understand? (Feel free to draw pictures if that would be helpful.)

Cube A has edges that are three times as long as the edges of cube B. The volume of cube A is 108 cubic centimeters. What is the volume of cube B?

Four gallons of paint were required to paint a scale model of a jet. The actual jet required 100 gallons of paint to be painted. What scale factor is associated with changing all of the length dimensions of the actual jet?

A right rectangular prism, which is 3 centimeters by 5 centimeters by 2 centimeters in size, is similar to a larger shape with a scale factor of 2. What is the total surface area of the larger shape?

Find the exact area of the figures below. A) B)

Ollie measures the area of his kitchen floor and finds that it is 2400 square decimeters. He needs to know how many square meters it is. Please help him by answering the question, and explain your response so that it will make sense to him. A diagram may be helpful.

What is the area of the figure below? (Use the natural unit.)

Bill used 8 gallons of paint to paint a reduced model of his airplane. His actual airplane is similar to the model, but five times as long. How many gallons of paint will Fred need to paint his actual airplane? (Hint: What characteristic is involved in painting the surface of a jet?)

State an appropriate unit of measurement for the following. A) the width of an airplane runway B) the amount of water in a bathtub C) the area covered by a painting D) the arc that the tip of a clock hand traces out as it moves from one number to the next

What is the area in square centimeters of the right triangle given below?

How is area different from volume? Can anything have area without having volume? Can anything have volume without having area? Give an example.

Reasoning About Quantities

Numeration Systems

Understanding Whole Number Operations

Some Conventional Ways of Computing

Using Numbers in Sensible Ways

Meanings for Fractions

Computing With Fractions

Multiplicative Comparisons and Multiplicative Reasoning

Ratios, Rates, Proportions, and Percents

Integers and Other Number Systems

Number Theory

What Is Algebra

A Quantitative Approach to Algebra and Graphing

Understanding Change: Relationships Among Time, Distance, and Rate

Further Topics in Algebra and Change

Polygons

Polyhedra

Symmetry

Tessellations

Similarity

Curves, Constructions, and Curved Surfaces

Transformation Geometry

Measurement Basics

Counting Units Fast: Measurement Formulas

Special Topics in Measurement

Quantifying Uncertainty

Determining More Complicated Probabilities

Introduction to Statistics and Sampling

Representing and Interpreting Data With One Variable

Dealing With Multiple Data Sets or With Multiple Variables

Variability in Samples

Special Topics in Probability

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