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Math Problems
Grade 6
Scale drawings: word problems
Ronnie made a scale drawing of a shopping center. A bakery in the shopping center is
7
7
7
inches wide in the drawing. The actual bakery is
42
42
42
feet wide. What is the scale of the drawing?
\newline
1
1
1
inch :
_
_
_
\_\_\_
___
feet
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8
8
8
. Mrs. Boothe told her class that the pencil is
2
/
3
2 / 3
2/3
yard in length. How long is the pencil Explain your answer with words and numbers.
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37
37
37
. What is the length of side
P
P
P
in the figure below?
25
cm
25\,\text{cm}
25
cm
P
P
P
20
cm
20\,\text{cm}
20
cm
\newline
A
6.7
cm
6.7\,\text{cm}
6.7
cm
\newline
B
11
cm
11\,\text{cm}
11
cm
\newline
C
15
cm
15\,\text{cm}
15
cm
\newline
D
45
cm
45\,\text{cm}
45
cm
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Eric made a scale drawing of the auditorium. The stage, which is
35
35
35
feet wide in real life, is
5
5
5
inches wide in the drawing. What is the scale of the drawing?
1
1
1
inch
‾
\underline{\quad}
feet
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7
7
7
. The figure below, not drawn to scale, is made up of a square MNOP and a rectangle PQRS. The length of the square is
6
c
m
6 \mathrm{~cm}
6
cm
. Find the area of the rectangle PQRS.
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Use the given scale factor and the side lengths of the scale drawing to determine the side lengths of the real object.
\newline
Scale factor:
3
:
1
3: 1
3
:
1
\newline
Scale drawing
\newline
a
\newline
Object
\newline
A. Side
a
a
a
is
7
7
7
inches long and side
b
b
b
is
6
6
6
inches long.
\newline
B. Side
a
a
a
is
63
63
63
inches long and side
b
b
b
is
54
54
54
inches long.
\newline
C. Side
a
a
a
is
18
18
18
inches long and side
b
b
b
is
15
15
15
inches long.
\newline
D. Side
a
a
a
is
24
24
24
inches long and side
b
b
b
is
21
21
21
inches long.
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Triangular pyramid
B
B
B
is the image of triangular pyramid
A
A
A
after dilation by a scale factor of
33
33
33
. If the surface area of triangular pyramid
A
A
A
is
55
in
2
55\,\text{in}^2
55
in
2
, find the surface area of triangular pyramid
B
B
B
, the image.
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7
7
7
\newline
Clear selectioı
\newline
1
1
1
.) A map has a scale of
1
/
2
1 / 2
1/2
inch
=
10
=10
=
10
miles. The distance between two
\newline
1
1
1
pol
\newline
schools is
2
2
2
.
75
75
75
inches. How far apart are the schools?
\newline
10
10
10
miles
\newline
13
13
13
.
75
75
75
miles
\newline
55
55
55
miles
\newline
20
20
20
miles
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A scale on a hiking map shows that
3
3
3
inches represents
1
1
1
.
25
25
25
miles.
\newline
What number of inches on the map represent
10
10
10
actual miles?
\newline
□
\square
□
inches
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Polygon
C
C
C
has an area of
40
40
40
square units. Kennan drew a scaled version of Polygon
C
C
C
using a scale factor of
1
2
\frac{1}{2}
2
1
and labeled it Polygon
D
D
D
.
\newline
What is the area of Polygon
D
D
D
?
\newline
□
\square
□
square units
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Background
\newline
Shape
\newline
Math
\newline
Canvas
\newline
Convert
\newline
Insert
\newline
Replay
\newline
Help
\newline
Brayden is making a scale model of an ant using a scale of
1
2
c
m
=
3
10
m
m
\frac{1}{2} \mathrm{~cm}=\frac{3}{10} \mathrm{~mm}
2
1
cm
=
10
3
mm
. Show your work. (
3
3
3
points)
\newline
A) If the length of the body of the actual ant is
6
6
6
millimeters, how long will the length of the body on the scale model be, in centimeters?
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What is the scale factor from the drawing to the actual airplane?
\newline
The scale factor is
2
2
2
\newline
What is the actual length of the wings of the the airplane from tip to tip?
\newline
?
m
\mathrm{m}
m
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What is the scale factor from the drawing to the actual airplane?
\newline
The scale factor is
\newline
2
2
2
\newline
What is the actual length of the wings of the the airplane from tip to tip?
\newline
?
m
\text { ? } \mathrm{m}
?
m
\newline
Scale Drawing
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Return
\newline
Tape Diagram
\newline
Use the following diagram to answer the questions
\newline
7
7
7
\newline
3
3
3
points
\newline
\begin{tabular}{|l|l|l|l|l|}
\newline
\hline
x
x
x
&
x
x
x
&
x
x
x
&
x
x
x
&
−
5
-5
−
5
\\
\newline
\hline
\newline
\end{tabular}
\newline
Write an equation for the diagram.
\newline
type your answer...
\newline
8
8
8
\newline
1
1
1
point
\newline
Solve the equation in question
7
7
7
.
\newline
x
=
\mathrm{x}=
x
=
\newline
Tape Diagram
\newline
Use the following diagram to answer the questions.
\newline
9
9
9
\newline
3
3
3
points
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Helen made a scale drawing of an office building. A desk, which is
6
6
6
feet long in real life, is
2
2
2
inches long in the drawing. What scale did Helen use for the drawing?
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To solve the equation
6
n
−
5
=
37
6 n-5=37
6
n
−
5
=
37
, Rishi decided to construct a table of values, and then plot a graph.
\newline
a) Complete Rishi's table of values for the equation.
\newline
\begin{tabular}{|l|l|l|l|l|l|}
\newline
\hline Term number
(
n
)
(n)
(
n
)
&
1
1
1
&
2
2
2
&
3
3
3
&
4
4
4
&
5
5
5
\\
\newline
\hline Term value
(
6
n
−
5
)
(6 n-5)
(
6
n
−
5
)
&
1
1
1
&
7
7
7
&
13
13
13
&
19
19
19
&
25
25
25
\\
\newline
\hline
\newline
\end{tabular}
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On a scale drawing, a distance of
1
1
1
foot is represented by a segment
0.25
0.25
0.25
inch in length. How long must a segment on the scale drawing be to represent a
36
36
36
-inch distance?
\newline
A.
0.25
0.25
0.25
in.
\newline
B.
0.75
0.75
0.75
in.
\newline
C.
9
9
9
in.
\newline
D.
144
144
144
in.
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Hung Lam plans to enclose a rectangular area for his chickens in his backyard using the sides of his apartment building for
2
2
2
of the sides, as seen in the figure. If Hung Lam has exactly
40
40
40
feet of chicken wire, what is the largest area, in square feet, he can enclose for his chickens?
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The rectangular floor of a classroom is
24
24
24
feet in length and
20
20
20
feet in width. A scale drawing of the floor has a length of
12
12
12
inches. What is the perimeter, in inches, of the floor in the scale drawing?
\newline
Answer:
□
\square
□
in.
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The rectangular floor of a classroom is
32
32
32
feet in length and
26
26
26
feet in width. A scale drawing of the floor has a length of
16
16
16
inches. What is the perimeter, in inches, of the floor in the scale drawing?
\newline
Answer:
□
\square
□
in.
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The rectangular floor of a classroom is
30
30
30
feet in length and
21
21
21
feet in width. A scale drawing of the floor has a length of
10
10
10
inches. What is the perimeter, in inches, of the floor in the scale drawing?
\newline
Answer:
□
\square
□
in.
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The rectangular floor of a classroom is
26
26
26
feet in length and
24
24
24
feet in width. A scale drawing of the floor has a length of
13
13
13
inches. What is the perimeter, in inches, of the floor in the scale drawing?
\newline
Answer:
□
\square
□
in.
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The rectangular floor of a classroom is
27
27
27
feet in length and
21
21
21
feet in width. A scale drawing of the floor has a length of
9
9
9
inches. What is the perimeter, in inches, of the floor in the scale drawing?
\newline
Answer:
□
\square
□
in.
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Polygon
C
C
C
has an area of
40
40
40
square units. Kennan drew a scaled version of Polygon
C
C
C
using a scale factor of
1
2
\frac{1}{2}
2
1
and labeled it Polygon
D
D
D
.
\newline
What is the area of Polygon
D
D
D
?
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It takes
b
b
b
minutes for Sylvia's bathtub to fill with water.
\newline
How many minutes will it take to fill
3
3
3
same-size bathtubs?
\newline
Write your answer as an expression.
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Circle
K
K
K
with a radius of
3
3
3
units is shown on a coordinate grid. Circle
K
K
K
is dillated by a scale factor of
5
3
\frac{5}{3}
3
5
, centered at the origin, to map to Circle
M
M
M
.
\newline
Complete the statement.
\newline
The area of the Circle
M
M
M
is
π
\pi
π
units
2
^2
2
.
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A right pentagonal prism is pictured below. Select the type of cross section formed when the figure is cut parallel to its base.
\newline
square
\newline
circle
\newline
hexagon
\newline
pentagon
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A triangle with a perimeter of
14
14
14
units is dilated by a scale factor of
3
3
3
. Find the perimeter of the triangle after dilation. Round your answer to the nearest tenth, if necessary.
\newline
Answer: units
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A square with an area of
6
6
6
units
2
^{2}
2
is dilated by a scale factor of
2
3
\frac{2}{3}
3
2
. Find the area of the square after dilation. Round your answer to the nearest tenth, if necessary.
\newline
Answer: units
2
^{2}
2
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A lake near the Arctic Circle is covered by sheet of ice during the cold winter months. When spring arrives, the ice starts to melt.
\newline
S
S
S
models the ice sheet's thickness (in meters) after
t
t
t
weeks.
\newline
S
=
−
0.25
t
+
4
S=-0.25t+4
S
=
−
0.25
t
+
4
\newline
What is the ice sheet's thickness at the beginning of spring?
\newline
m
e
t
e
r
s
meters
m
e
t
ers
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