Deck 24: Area, Surface Area, and Volume

Question 1

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:

Answer 1

A) 6
B) 12

Question 2

There are _____ square decimeters in 9 square centimeters.

Answer 2

0.09

Question 3

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.)

Answer 3

Sketching a picture of an actual 2 square yards, marked in square feet, might be the best answer.

Question 4

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

Question 5

Juan, Kim, and Angelo each measured the area of a surface using the following units of measure (shaded).
Which set of measurements could they came up with?

A) Juan: 60 units; Kim: 15 units; Angelo: 90 units
B) Juan: 60 units; Kim: 240 units; Angelo: 40 units
C) Juan: 60 units; Kim: 160 units; Angelo: 50 units
D) Juan: 40 units; Kim: 30 units; Angelo: 80 units

Question 6

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.

Question 7

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?

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

Question 8

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

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

Question 9

A Pringles can has a height of 30 centimeters and a diameter of 8 centimeters. The height of each Pringle is 0.25 centimeters. If we assume that the Pringles are flat, what is the total number of Pringles that will fit in the can?

A) $\frac { 8 \pi } { 3 }$ Pringles
B) 120 Pringles
C) 60 Pringles
D) 8 Pringles

Question 10

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?

Question 11

Determine the area of the shaded region on the given geoboard if the unit of measurement is one square centimeter. Use correct units.

Question 12

Find the exact area of the figures below.

A)


B)

Question 13

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?

Question 14

Elizabeth measures the area of her bedroom floor and finds that it is 1116 square decimeters. How many square meters is it?

A) 1.1 square meters
B) 11.16 square meters
C) 111.6 square meters
D) There is not enough information to answer the question.

Question 15

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

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 16

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

Question 17

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

Question 18

For each statement, indicate the MOST appropriate measurement.

A) The area of one page in a telephone book is about:
$\quad$$\quad$$\quad$$\quad$ 6 cm² $\quad$ 6 dm² $\quad$ 6 mm²

B) The floor area in a small classroom is about:
$\quad$$\quad$$\quad$$\quad$ 80 mm² $\quad$ 80 dm² $\quad$ 80m²

C) The amount of water in the lake is about:
$\quad$$\quad$$\quad$$\quad$ 14km $\quad$ 14km² $\quad$ 14km³

D) The volume of a slice of bread is about:
$\quad$$\quad$$\quad$$\quad$ 102cm³ $\quad$ 102dm³ $\quad$ 102 mm³

Question 19

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?)

Question 20

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

Question 21

Convert the following.

A) 5 g = _____ mg
B) 27 cm² = _____ m²
C) 1 m³ = _____ cm³

Question 22

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

Question 23

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 }$

Question 24

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

Question 25

How is surface area different from volume? Your explanation may include an example, but make it clear how the ideas, not just the numbers, are different.

Question 26

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.)

Question 27

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?

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