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Math Problems
Grade 6
Evaluate variable expressions: word problems
The lengths of the four sides of a quadrilateral (in centimeters) are consecutive integers. If the perimeter is
46
46
46
centimeters, find the value of the longest of the four side lengths.
\newline
Answer: centimeters
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The lengths of the three sides of a triangle (in meters) are consecutive odd integers. If the perimeter is
93
93
93
meters, find the value of the shortest of the three side lengths.
\newline
Answer: meters
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The lengths of the three sides of a triangle (in inches) are consecutive integers. If the perimeter is
75
75
75
inches, find the value of the middle of the three side lengths.
\newline
Answer: inches
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The lengths of the three sides of a triangle (in meters) are consecutive even integers. If the perimeter is
96
96
96
meters, find the value of the shortest of the three side lengths.
\newline
Answer: meters
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A man starts walking north at
2
ft/s
2\,\text{ft/s}
2
ft/s
from a point
P
P
P
. Five minutes later a woman starts walking south at
5
ft/s
5\,\text{ft/s}
5
ft/s
from a point
500
ft
500\,\text{ft}
500
ft
due east of
P
P
P
. At what rate are the woman and man separating when the woman starts walking? (Round your answer to two decimal places.)
\newline
Enter a number:______
ft/s
\text{ft/s}
ft/s
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Find the volume of a right circular cone that has a height of
11
11
11
.
2
2
2
in
\text{in}
in
and a base with a circumference of
12
12
12
.
6
6
6
in
\text{in}
in
. Round your answer to the nearest tenth of a cubic inch.
\newline
Answer:
in
\text{in}
in
3
^{3}
3
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Find the volume of a right circular cone that has a height of
11
11
11
.
7
7
7
in
\text{in}
in
and a base with a circumference of
18.8
18.8
18.8
i
n
\mathrm{in}
in
. Round your answer to the nearest tenth of a cubic inch.
\newline
Answer:
in
\text{in}
in
3
^{3}
3
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Find the volume of a pyramid with a square base, where the perimeter of the base is
9
f
t
9 \mathrm{ft}
9
ft
and the height of the pyramid is
6.4
f
t
6.4 \mathrm{ft}
6.4
ft
. Round your answer to the nearest tenth of a cubic foot.
\newline
Answer:
f
t
3
\mathrm{ft}^{3}
ft
3
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Find the volume of a pyramid with a square base, where the area of the base is
16.6
i
n
2
16.6 \mathrm{in}^{2}
16.6
in
2
and the height of the pyramid is
20.9
i
n
20.9 \mathrm{in}
20.9
in
. Round your answer to the nearest tenth of a cubic inch.
\newline
Answer: in
3
^{3}
3
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Find the volume of a pyramid with a square base, where the area of the base is
7.7
m
2
7.7 \mathrm{~m}^{2}
7.7
m
2
and the height of the pyramid is
4.2
m
4.2 \mathrm{~m}
4.2
m
. Round your answer to the nearest tenth of a cubic meter.
\newline
Answer:
m
3
\mathrm{m}^{3}
m
3
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Find the volume of a pyramid with a square base, where the area of the base is
19.3
f
t
2
19.3 \mathrm{ft}^{2}
19.3
ft
2
and the height of the pyramid is
25.3
f
t
25.3 \mathrm{ft}
25.3
ft
. Round your answer to the nearest tenth of a cubic foot.
\newline
Answer:
f
t
3
\mathrm{ft}^{3}
ft
3
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Find the volume of a pyramid with a square base, where the side length of the base is
18
18
18
.
2
2
2
in and the height of the pyramid is
12.2
i
n
12.2 \mathrm{in}
12.2
in
. Round your answer to the nearest tenth of a cubic inch.
\newline
Answer: in
3
^{3}
3
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Find the volume of a pyramid with a square base, where the side length of the base is
13
13
13
.
2
2
2
in and the height of the pyramid is
7.3
i
n
7.3 \mathrm{in}
7.3
in
. Round your answer to the nearest tenth of a cubic inch.
\newline
Answer: in
3
^{3}
3
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Find the volume of a pyramid with a square base, where the perimeter of the base is
4.2
f
t
4.2 \mathrm{ft}
4.2
ft
and the height of the pyramid is
4.7
f
t
4.7 \mathrm{ft}
4.7
ft
. Round your answer to the nearest tenth of a cubic foot.
\newline
Answer:
f
t
3
\mathrm{ft}^{3}
ft
3
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Find the volume of a pyramid with a square base, where the perimeter of the base is
9.4
f
t
9.4 \mathrm{ft}
9.4
ft
and the height of the pyramid is
6.2
f
t
6.2 \mathrm{ft}
6.2
ft
. Round your answer to the nearest tenth of a cubic foot.
\newline
Answer:
f
t
3
\mathrm{ft}^{3}
ft
3
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Find the volume of a pyramid with a square base, where the area of the base is
6.9
f
t
2
6.9 \mathrm{ft}^{2}
6.9
ft
2
and the height of the pyramid is
3.1
f
t
3.1 \mathrm{ft}
3.1
ft
. Round your answer to the nearest tenth of
a
a
a
cubic foot.
\newline
Answer:
f
t
3
\mathrm{ft}^{3}
ft
3
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What is the volume of a hemisphere with a diameter of
5
m
5 \mathrm{~m}
5
m
, rounded to the nearest tenth of a cubic meter?
\newline
Answer:
m
3
\mathrm{m}^{3}
m
3
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Find the volume of a right circular cone that has a height of
9.6
m
9.6 \mathrm{~m}
9.6
m
and a base with a radius of
2.1
m
2.1 \mathrm{~m}
2.1
m
. Round your answer to the nearest tenth of a cubic meter.
\newline
Answer:
m
3
\mathrm{m}^{3}
m
3
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Find the volume of a right circular cone that has a height of
14.2
m
14.2 \mathrm{~m}
14.2
m
and a base with a radius of
16
m
16 \mathrm{~m}
16
m
. Round your answer to the nearest tenth of a cubic meter.
\newline
Answer:
m
3
\mathrm{m}^{3}
m
3
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Find the volume of a right circular cone that has a height of
9.2
f
t
9.2 \mathrm{ft}
9.2
ft
and a base with a circumference of
7.6
f
t
7.6 \mathrm{ft}
7.6
ft
. Round your answer to the nearest tenth of a cubic foot.
\newline
Answer:
f
t
3
\mathrm{ft}^{3}
ft
3
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Find the volume of a right circular cone that has a height of
13.7
f
t
13.7 \mathrm{ft}
13.7
ft
and a base with a circumference of
18.4
f
t
18.4 \mathrm{ft}
18.4
ft
. Round your answer to the nearest tenth of a cubic foot.
\newline
Answer:
f
t
3
\mathrm{ft}^{3}
ft
3
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Find the volume of a right circular cone that has a height of
5.1
c
m
5.1 \mathrm{~cm}
5.1
cm
and a base with a radius of
17.5
c
m
17.5 \mathrm{~cm}
17.5
cm
. Round your answer to the nearest tenth of a cubic centimeter.
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Find the volume of a right circular cone that has a height of
10.4
m
10.4 \mathrm{~m}
10.4
m
and a base with a radius of
4.9
m
4.9 \mathrm{~m}
4.9
m
. Round your answer to the nearest tenth of a cubic meter.
\newline
Answer:
m
3
\mathrm{m}^{3}
m
3
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If
2
x
=
−
1
+
y
−
x
y
2x = -1 + y - xy
2
x
=
−
1
+
y
−
x
y
then find the equations of all tangent lines to the curve when
y
=
−
5.
y = -5.
y
=
−
5.
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