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Math Problems
Grade 7
Convert between customary and metric systems
For a sample of stomach acid that is
3.13
×
1
0
−
2
M
3.13 \times 10^{-2} \ M
3.13
×
1
0
−
2
M
in
HCl
\text{HCl}
HCl
, how many moles of
HCl
\text{HCl}
HCl
are in
14.1
mL
14.1 \ \text{mL}
14.1
mL
of the stomach acid? Express the amount to three significant figures and include the appropriate units.
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Hundredth:
45
45
45
.
880
880
880
\newline
Round each number to
t
t
t
\newline
1
1
1
.
4
4
4
.
38
38
38
\newline
00
00
00
\newline
2
2
2
.
8
8
8
.
4
4
4
\newline
3
3
3
.
54
54
54
.
076
076
076
\newline
Round each number to
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9
9
9
liters is the same as how many gallons?
\newline
Hint:
1
L
≈
0.26
gal
1 \, \text{L} \approx 0.26 \, \text{gal}
1
L
≈
0.26
gal
\newline
Round your answer to the nearest tenth.
\newline
__________
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How many gallons are there in
6
L
6\,\text{L}
6
L
?
\newline
Hint:
1
L
≈
0.26
gal
1\,\text{L} \approx 0.26\,\text{gal}
1
L
≈
0.26
gal
\newline
Round your answer to the nearest tenth.
\newline
_________
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6
6
6
centimeters is the same as how many inches?
\newline
Hint:
1
1
1
cm
≈
0.39
\approx 0.39
≈
0.39
in
\newline
Round your answer to the nearest tenth.
\newline
____________
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How many kilograms are there in
10
10
10
pounds?
\newline
Hint:
1
lb
≈
0.454
kg
1 \, \text{lb} \approx 0.454 \, \text{kg}
1
lb
≈
0.454
kg
\newline
Round your answer to the nearest tenth.
\newline
_________
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How many gallons are there in
10
10
10
liters?
\newline
Hint:
\newline
1
L
≈
0.26
gal
1\,\text{L}\approx0.26\,\text{gal}
1
L
≈
0.26
gal
\newline
Round your answer to the nearest tenth.
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What is the volume of a hemisphere with a radius of
6.5
i
n
6.5 \mathrm{in}
6.5
in
, rounded to the nearest tenth of a cubic inch?
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How many ounces are there in
8
grams
8\,\text{grams}
8
grams
?
\newline
Hint:
1
g
≈
0.035
oz
1\,\text{g} \approx 0.035\,\text{oz}
1
g
≈
0.035
oz
\newline
Round your answer to the nearest tenth.
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5
5
5
milliliters is how many teaspoons?
\newline
Hint:
1
1
1
mL
≈
0.2
\approx 0.2
≈
0.2
tsp
\newline
Round your answer to the nearest tenth.
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4
4
4
kilograms is the same as how many pounds?
\newline
Hint:
1
1
1
kg
≈
2.2
\approx 2.2
≈
2.2
lb
\newline
Round your answer to the nearest tenth.
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How many gallons are there in
3
3
3
liters?
\newline
Hint:
1
L
≈
0.26
gal
1 \, \text{L} \approx 0.26 \, \text{gal}
1
L
≈
0.26
gal
\newline
Round your answer to the nearest tenth.
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2
2
2
liters is the same as how many gallons?
\newline
Hint:
1
L
≈
0.26
gal
1 \text{ L} \approx 0.26 \text{ gal}
1
L
≈
0.26
gal
\newline
Round your answer to the nearest tenth.
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8
8
8
pounds is the same as how many kilograms?
\newline
Hint:
1
1
1
lb
≈
0.454
\approx 0.454
≈
0.454
kg
\newline
Round your answer to the nearest tenth.
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2
2
2
kilometers is how many miles?
\newline
Hint:
1
1
1
km
≈
0.6
\approx 0.6
≈
0.6
mi
\newline
Round your answer to the nearest tenth.
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10
10
10
feet is the same as how many meters?
\newline
Hint:
1
1
1
ft
≈
0.305
\approx 0.305
≈
0.305
m
\newline
Round your answer to the nearest tenth.
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What is the total number of different
10
10
10
-letter arrangements that can be formed using the letters in the word SUFFRAGIST?
\newline
Answer:
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What is the total number of different
12
12
12
-letter arrangements that can be formed using the letters in the word ANNUNCIATION?
\newline
Answer:
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What is the total number of different
11
11
11
-letter arrangements that can be formed using the letters in the word GALVANIZING?
\newline
Answer:
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What is the total number of different
6
6
6
-letter arrangements that can be formed using the letters in the word QUASAR?
\newline
Answer:
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What is the total number of different
8
8
8
-letter arrangements that can be formed using the letters in the word ZIGGURAT?
\newline
Answer:
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A rectangular garden whose width is
4
4
4
meters less than its length has an area of
57
57
57
square meters. Find the dimensions of the garden to the nearest tenth of a meter.
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Standard movie projectors project
24
24
24
still images, known as frames, each second. If a certain movie uses the standard frame rate and has exactly
129600
129600
129600
total frames, then, to the nearest whole minute, how long is the movie?
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How many packets of milk having capacity of
250
m
l
250 \mathrm{ml}
250
ml
can be packed from
10
10
10
litre amount of milk.
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The area of a parallelogram is
3094
3094
3094
, and the lengths of its sides are
73
73
73
and
52
52
52
. Determine, to the nearest tenth of a degree, the measure of the obtuse angle of the parallelogram.
\newline
Answer:
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The area of a parallelogram is
4
4
4
, and the lengths of its sides are
2
2
2
.
8
8
8
and
2
2
2
. Determine, to the nearest tenth of a degree, the measure of the obtuse angle of the parallelogram.
\newline
Answer:
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The area of a triangle is
4
4
4
. Two of the side lengths are
7
7
7
.
5
5
5
and
1
1
1
.
6
6
6
and the included angle is obtuse. Find the measure of the included angle, to the nearest tenth of a degree.
\newline
Answer:
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The areas of two mathematically similar shapes are in the ratio
49
:
81
49:81
49
:
81
. The length of the smaller shape is
24.5
cm
24.5\,\text{cm}
24.5
cm
. Work out the length of the larger shape.
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A mold culture covering
125
c
m
2
125 \mathrm{~cm}^{2}
125
cm
2
shrinks to two-fifths of the previous day's size each day. How big is mold culture after five days?
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If the volume of a right circular cylinder with a radius of
4
4
4
feet and a height of
30
30
30
feet is
a
π
a\pi
aπ
cubic feet, what is the value of
a
a
a
?
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What is the volume of a hemisphere with a radius of
55.8
55.8
55.8
i
n
\mathrm{in}
in
, rounded 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
14
14
14
in
\text{in}
in
and a base with a radius of
9
9
9
.
1
1
1
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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What is the volume of a sphere with a diameter of
6
6
6
.
7
7
7
in
\text{in}
in
, rounded to the nearest tenth of a cubic inch?
\newline
Answer:
in
\text{in}
in
3
^{3}
3
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In a lab experiment,
30
30
30
bacteria are placed in a petri dish. The conditions are such that the number of bacteria is able to double every
7
7
7
hours. How many bacteria would there be after
16
16
16
hours, to the nearest whole number?
\newline
Answer:
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In a lab experiment,
40
40
40
bacteria are placed in a petri dish. The conditions are such that the number of bacteria is able to double every
28
28
28
hours. How many bacteria would there be after
10
10
10
hours, to the nearest whole number?
\newline
Answer:
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In a lab experiment,
6300
6300
6300
bacteria are placed in a petri dish. The conditions are such that the number of bacteria is able to double every
8
8
8
hours. How many bacteria would there be after
19
19
19
hours, to the nearest whole number?
\newline
Answer:
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In a lab experiment,
30
30
30
bacteria are placed in a petri dish. The conditions are such that the number of bacteria is able to double every
14
14
14
hours. How many bacteria would there be after
4
4
4
hours, to the nearest whole number?
\newline
Answer:
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In a lab experiment,
10
10
10
bacteria are placed in a petri dish. The conditions are such that the number of bacteria is able to double every
13
13
13
hours. How many bacteria would there be after
19
19
19
hours, to the nearest whole number?
\newline
Answer:
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In a lab experiment,
400
400
400
bacteria are placed in a petri dish. The conditions are such that the number of bacteria is able to double every
28
28
28
hours. How many bacteria would there be after
30
30
30
hours, to the nearest whole number?
\newline
Answer:
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In a lab experiment,
70
70
70
bacteria are placed in a petri dish. The conditions are such that the number of bacteria is able to double every
15
15
15
hours. How many bacteria would there be after
29
29
29
hours, to the nearest whole number?
\newline
Answer:
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A flywheel with a
15
−
c
m
15-\mathrm{cm}
15
−
cm
diameter is rotating at a rate of
7
7
7
radians
/
s
e
c
/ \mathrm{sec}
/
sec
. What is the linear speed of a point on its rim, in centimeters per minute?
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What is the volume of a hemisphere with a radius of
8
8
8
in
\text{in}
in
, rounded to the nearest tenth of a cubic inch?
\newline
Answer:
in
\text{in}
in
3
^{3}
3
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What is the volume of a cylinder, in cubic centimeters, with a height of
18
18
18
centimeters and a base diameter of
8
8
8
centimeters? Round to the nearest tenths place
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The distance from Uranus to Jupiter is
2.092
×
1
0
9
2.092 \times 10^{9}
2.092
×
1
0
9
kilometers. How long would it take a rocket, traveling at
2.5
×
1
0
4
2.5 \times 10^{4}
2.5
×
1
0
4
kilometers per hour to travel from Uranus to Jupiter? Round your answer to the nearest whole number of hours.
\newline
Answer: ____hours
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Find the volume of a right circular cone that has a height of
16
16
16
.
6
6
6
in
\text{in}
in
and a base with a circumference of
4.8
4.8
4.8
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
15
15
15
.
5
5
5
in
\text{in}
in
and a base with a circumference of
16.8
16.8
16.8
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 side length of the base is
13.3
f
t
13.3 \mathrm{ft}
13.3
ft
and the height of the pyramid is
18.1
f
t
18.1 \mathrm{ft}
18.1
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
15.3
c
m
15.3 \mathrm{~cm}
15.3
cm
and the height of the pyramid is
9.5
c
m
9.5 \mathrm{~cm}
9.5
cm
. Round your answer to the nearest tenth of a cubic centimeter.
\newline
Answer:
c
m
3
\mathrm{cm}^{3}
cm
3
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Find the volume of a pyramid with a square base, where the area of the base is
17.5
f
t
2
17.5 \mathrm{ft}^{2}
17.5
ft
2
and the height of the pyramid is
14.4
f
t
14.4 \mathrm{ft}
14.4
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 side length of the base is
12.9
c
m
12.9 \mathrm{~cm}
12.9
cm
and the height of the pyramid is
6.2
c
m
6.2 \mathrm{~cm}
6.2
cm
. Round your answer to the nearest tenth of a cubic centimeter.
\newline
Answer:
c
m
3
\mathrm{cm}^{3}
cm
3
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