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Math Problems
Grade 6
Volume of cubes and rectangular prisms: word problems
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\newline
Indicates required question
\newline
Puzzle
4
4
4
\newline
Can you find the slope-intercept equation of each line and type the correct code? * Please remember to type in ALL CAPS with no spaces.
\newline
Your answer
\newline
This is a required question
\newline
Clear form
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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
.
5
5
5
in and the height of the pyramid is
10
10
10
.
9
9
9
in. Round your answer to the nearest tenth of a cubic inch.
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Consider the following data on the length of eggs (mm) of two breeds of cuckoo
22.5
22.5
22.5
20.1
20.1
20.1
23.3
23.3
23.3
22.9
22.9
22.9
22.0
22.0
22.0
23.1
23.1
23.1
22.0
22.0
22.0
22.3
22.3
22.3
23.6
23.6
23.6
24.7
24.7
24.7
20.1
20.1
20.1
0
0
0
20.1
20.1
20.1
1
1
1
20.1
20.1
20.1
2
2
2
20.1
20.1
20.1
3
3
3
20.1
20.1
20.1
4
4
4
20.1
20.1
20.1
5
5
5
20.1
20.1
20.1
6
6
6
20.1
20.1
20.1
20.1
20.1
20.1
8
8
8
20.1
20.1
20.1
8
8
8
22.5
22.5
22.5
22.3
22.3
22.3
20.1
20.1
20.1
8
8
8
22.0
22.0
22.0
20.1
20.1
20.1
5
5
5
23.3
23.3
23.3
23.3
23.3
23.3
6
6
6
22.3
22.3
22.3
23.3
23.3
23.3
8
8
8
20.1
20.1
20.1
0
0
0
22.0
22.0
22.0
22.9
22.9
22.9
1
1
1
23.3
23.3
23.3
6
6
6
22.9
22.9
22.9
3
3
3
22.9
22.9
22.9
4
4
4
23.3
23.3
23.3
20.1
20.1
20.1
1
1
1
23.6
23.6
23.6
22.9
22.9
22.9
8
8
8
22.9
22.9
22.9
a. Use a class interval of size
22.0
22.0
22.0
0
0
0
, construct a grouped frequency distribution. b. Find first and third Quartile of the distribution c. Obtain the mean and standard deviation d. Show whether second quartile is same as the median of the distribution and comment on your result.
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A human hair is approximately
40
40
40
microns
(
μ
m
)
(\mu \mathrm{m})
(
μ
m
)
wide. If
1
μ
m
1 \mu \mathrm{m}
1
μ
m
is equal to
1
0
−
6
10^{-6}
1
0
−
6
meters
(
m
)
(\mathrm{m})
(
m
)
, and
1
1
1
nanometer
(
n
m
)
(\mathrm{nm})
(
nm
)
is equal to
1
0
−
9
m
10^{-9} \mathrm{~m}
1
0
−
9
m
, then how many nanometers wide is a human hair?
\newline
Choose
1
1
1
answer:
\newline
(A)
0.0004
n
m
0.0004 \mathrm{~nm}
0.0004
nm
\newline
(B)
0.004
n
m
0.004 \mathrm{~nm}
0.004
nm
\newline
(c)
4
,
000
n
m
4,000 \mathrm{~nm}
4
,
000
nm
\newline
(D)
40
,
000
n
m
40,000 \mathrm{~nm}
40
,
000
nm
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Glven the SLANT height, find the height of the cone, then find the volume of the cone. Include the correct units for each:
\newline
Height of cone
=
=
=
\qquad
\newline
Volume of cone
=
=
=
\qquad
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find the volume of a regular hexagonal pyramid with side length
15
15
15
meters and a lateral edge of
17
17
17
meters
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ASSIGNMENTS ; CIRCLES TEST
\newline
=
1
1
1
STUDY GUIDE
\newline
5
5
5
The circle graph gives the percentage of students who favor the different lunch menus offered by the school cafeteria. Find the
\newline
m
J
M
‾
∠
m\overline{JM}^{\angle}
m
J
M
∠
.
\newline
The
m
J
M
‾
∠
m\overline{JM}^{\angle}
m
J
M
∠
is
\newline
□
\square
□
degrees.
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Determine if the line is or is not a tangent line to the circle.
\newline
*Tangent
\newline
Not a tangent
\newline
Option
3
3
3
\newline
Determine if the line is or is not a tangent line to the circle.
\newline
6.6
6.6
6.6
\newline
B
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The perimeter
p
p
p
of the rectangle below is
30
30
30
inches. Which formula can be used to find the length and width of the rectangle?
\newline
A
p
=
w
+
(
w
+
3
)
p = w + (w + 3)
p
=
w
+
(
w
+
3
)
\newline
B
p
=
w
(
w
+
3
)
p = w(w + 3)
p
=
w
(
w
+
3
)
\newline
C
p
=
2
w
+
2
(
w
+
3
)
p = 2w + 2(w + 3)
p
=
2
w
+
2
(
w
+
3
)
\newline
D
p
=
2
(
w
+
3
)
−
2
w
p = 2(w + 3) - 2w
p
=
2
(
w
+
3
)
−
2
w
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Molly built a teepee in the shape of a cone. The diameter of the base is
12
12
12
feet and the height is
18
18
18
feet. What is the volume of the cone?
\newline
A
72
π
cu ft
72\pi \, \text{cu ft}
72
π
cu ft
\newline
B
216
π
cu ft
216\pi \, \text{cu ft}
216
π
cu ft
\newline
C
648
π
cu ft
648\pi \, \text{cu ft}
648
π
cu ft
\newline
D
864
π
cu ft
864\pi \, \text{cu ft}
864
π
cu ft
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A cylinder has a radius of
4.8
4.8
4.8
feet and a height of
8.1
8.1
8.1
feet. What is the volume, to the nearest tenth of a cubic foot, of the cylinder?
\newline
(A)
989.4
\quad989.4
989.4
\newline
(B)
586.3
\quad586.3
586.3
\newline
(C)
244.3
\quad244.3
244.3
\newline
(D)
186.6
\quad186.6
186.6
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A paint can is dropped from the top of a building
51
51
51
.
84
84
84
feet above the ground. So,
51
51
51
.
84
84
84
feet is the can's maximum height. After
0
0
0
.
5
5
5
seconds, the can is
47
47
47
.
84
84
84
feet above the ground. The can hits the ground
1
1
1
.
8
8
8
seconds after it is dropped.
\newline
Let
f
(
x
)
f(x)
f
(
x
)
be the height (in feet) of the can
x
x
x
seconds after it is dropped. Then, the function
f
f
f
is guadratic. (Its graph is a parabola with vertex (
0
,
51.84
)
0,51.84)
0
,
51.84
)
.) Write an equation for the quadratic function
f
f
f
.
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2
2
2
. Here are the masses of the so-called inner planets of the solar system.
\newline
Mercury:
3.3022
×
1
0
23
k
g
3.3022 \times 10^{23} \mathrm{~kg}
3.3022
×
1
0
23
kg
\newline
Venus:
4.8685
×
1
0
24
k
g
4.8685 \times 10^{24} \mathrm{~kg}
4.8685
×
1
0
24
kg
\newline
Earth:
5.9722
×
1
0
24
k
g
5.9722 \times 10^{24} \mathrm{~kg}
5.9722
×
1
0
24
kg
\newline
Mars:
6.4185
×
1
0
23
k
g
6.4185 \times 10^{23} \mathrm{~kg}
6.4185
×
1
0
23
kg
\newline
What is the average mass of all four inner planets? Write your answer in sci
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Virginia State Standards of Learning Selence, Math and Technology Practice Tests
\newline
Start Over
\newline
Start over
\newline
Slart Over
\newline
WewResults
\newline
Read Exptanation
\newline
Skp Question
\newline
Question Number
2
2
2
of
40
40
40
-
8
8
8
th Grade Math
\newline
A rectangular photograph measured
7
7
7
.
5
5
5
centimeters wide and
10
10
10
.
0
0
0
centimeters long. An enlargement was made hat was
22
22
22
.
5
5
5
centimeters wide. How long was the enlargement?
\newline
(F)
17.5
c
m
17.5 \mathrm{~cm}
17.5
cm
\newline
(c)
75.0
c
m
75.0 \mathrm{~cm}
75.0
cm
\newline
(
11
11
11
)
225.0
c
m
225.0 \mathrm{~cm}
225.0
cm
\newline
(
1
1
1
)
30.0
c
m
30.0 \mathrm{~cm}
30.0
cm
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How deep is a rectangular pool that is
24
f
t
24 \mathrm{ft}
24
ft
. long and
15
f
t
15 \mathrm{ft}
15
ft
. wide and has a volume of
1
1
1
,
620
620
620
cubic feet?
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A micron is a metric unit used to measure microscopic lengths. It is represented by the symbol
μ
m
\mu m
μ
m
and is equal to about
0.000039
0.000039
0.000039
inches. What is the approximate size of one micron written in scientific notation?
\newline
Choices:
\newline
(A)
4
×
1
0
−
4
4 \times 10^{-4}
4
×
1
0
−
4
inches
\newline
(B)
4
×
1
0
−
5
4 \times 10^{-5}
4
×
1
0
−
5
inches
\newline
(C)
4
×
1
0
−
6
4 \times 10^{-6}
4
×
1
0
−
6
inches
\newline
(D)
4
×
1
0
−
7
4 \times 10^{-7}
4
×
1
0
−
7
inches
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The largest U.S. state is Alaska, which covers
5.7
×
1
0
5
5.7 \times 10^5
5.7
×
1
0
5
square miles. Rhode Island, the smallest state, covers
1
×
1
0
3
1 \times 10^3
1
×
1
0
3
square miles. How many times as big as Rhode Island is Alaska? Write your answer in standard form. Do not use exponents.
\newline
____ times as big
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The miles of track in the U.S. railroad system peaked in the early
1900
1900
1900
s. At that time, more than
270
,
000
270,000
270
,
000
miles of track crisscrossed the country. What is the approximate amount of track written in scientific notation?
\newline
Choices:
\newline
(A)
3
×
1
0
4
3 \times 10^4
3
×
1
0
4
miles
\newline
(B)
3
×
1
0
5
3 \times 10^5
3
×
1
0
5
miles
\newline
(C)
3
×
1
0
6
3 \times 10^6
3
×
1
0
6
miles
\newline
(D)
3
×
1
0
7
3 \times 10^7
3
×
1
0
7
miles
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A penny is
6
×
1
0
−
2
6 \times 10^{-2}
6
×
1
0
−
2
inches thick. The Empire State Building has a height of
1
,
250
1,250
1
,
250
feet, or
1.5
×
1
0
4
1.5 \times 10^{4}
1.5
×
1
0
4
inches. How many pennies would you have to stack to reach the top of the Empire State Building?
\newline
Write your answer in scientific notation.
\newline
______ pennies
\newline
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A typical business card is
0.013
0.013
0.013
inches thick. How would you write the approximate thickness in scientific notation?
\newline
Choices:
\newline
(A)
1
×
1
0
2
1 \times 10^2
1
×
1
0
2
inches
\newline
(B)
1
×
1
0
−
2
1 \times 10^{-2}
1
×
1
0
−
2
inches
\newline
(C)
1
×
1
0
3
1 \times 10^3
1
×
1
0
3
inches
\newline
(D)
1
×
1
0
−
3
1 \times 10^{-3}
1
×
1
0
−
3
inches
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Find the volume of a pyramid with a square base, where the side length of the base is
14.4
m
14.4 \mathrm{~m}
14.4
m
and the height of the pyramid is
15.3
m
15.3 \mathrm{~m}
15.3
m
. Round your answer to the nearest tenth of a cubic meter.
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A covered water tank is in the shape of a cylinder. The tank has a
28
28
28
-inch diameter and a height of
66
66
66
inches. To the nearest square inch, what is the surface area of the water tank?
\newline
A.
1
1
1
,
848
848
848
\newline
B.
7
7
7
,
037
037
037
\newline
C.
16
16
16
,
537
537
537
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What's the volume of this cube: height= ext{
1
1
1
inch}, length= rac{
1
1
1
}{
2
2
2
} ext{ inch}, and width= rac{
1
1
1
}{
4
4
4
} ext{ inch} and provide answer in fraction?
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Manager Mark counted the number of innings each Shire Sharks pitcher pitched during the Soiltop Tournament. Calvin pitched
11
11
11
innings, Brody pitched
5
5
5
innings, Thom pitched
12
12
12
innings, Shawn pitched
7
7
7
innings, and Harley pitched
5
5
5
innings.
\newline
Find the mean absolute deviation (MAD) of the data set.
\newline
□
\square
□
innings
\text{innings}
innings
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An outdoor light illuminates a circular region on the ground. The illuminated region has a diameter of
18
18
18
feet. The bulb has a shield that allows an illuminated arc which measures
12
0
∘
120^\circ
12
0
∘
. What is the area the light can illuminate? Give your answer in terms of
π
\pi
π
.
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A
\newline
c
\newline
B
\newline
D
\newline
The surface area of a cube is
294
i
n
2
294 \mathrm{in}^{2}
294
in
2
.
\newline
What is the length, in inches, of one side of the cube?
\newline
A)
6
6
6
\newline
B)
7
7
7
\newline
C)
8
8
8
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A
\newline
c
\newline
B)
\newline
D
\newline
The surface area of a cube is
294
i
n
2
294 \mathrm{in}^{2}
294
in
2
.
\newline
What is the length, in inches, of one side of the cube?
\newline
A)
6
6
6
\newline
B)
7
7
7
\newline
C)
8
8
8
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A rectangular prism and cube have equal volumes. The length of the rectangular prism is
12
cm
12\,\text{cm}
12
cm
and its width is
8
cm
8\,\text{cm}
8
cm
. If each side of the cube is
12
cm
12\,\text{cm}
12
cm
, then what is the height of the rectangular prism in centimeters?
\newline
□
\square
□
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it
6
6
6
B Review Guide
\newline
Google Docs
\newline
E/
1
1
1
FA pQLSdidk
1
1
1
wTqog
1
1
1
nnRXnGNcHRMndiM_CZggJIGZ-Y-K-Eb_h
82
82
82
po/wiewform
\newline
What is the volume of the triangular prism below? *
\newline
1
1
1
\newline
Your answer
\newline
What is the volume of the cereal box in the shape of a rectangular prism? *
\newline
1
1
1
po
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Nora uploaded a funny video on her website, which rapidly gains views over time. The following function gives the number of views
t
t
t
days after Nora uploaded the video:
\newline
V
(
t
)
=
100
⋅
e
0.4
t
V(t)=100 \cdot e^{0.4 t}
V
(
t
)
=
100
⋅
e
0.4
t
\newline
What is the instantaneous rate of change of the number of views
4
4
4
days after the video was uploaded?
\newline
Choose
1
1
1
answer:
\newline
(A)
198
198
198
views
\newline
(B)
198
198
198
views per day
\newline
(C)
495
495
495
views
\newline
(D)
495
495
495
views per day
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The side of the base of a square prism is increasing at a rate of
5
5
5
meters per second and the height of the prism is decreasing at a rate of
2
2
2
meters per second.
\newline
At a certain instant, the base's side is
6
6
6
meters and the height is
7
7
7
meters.
\newline
What is the rate of change of the volume of the prism at that instant (in cubic meters per second)?
\newline
Choose
1
1
1
answer:
\newline
(A)
348
348
348
\newline
(B)
−
492
-492
−
492
\newline
(C)
−
348
-348
−
348
\newline
(D)
492
492
492
\newline
The volume of a square prism with base side
s
s
s
and height
h
h
h
is
s
2
h
s^{2} h
s
2
h
.
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The radius of the base of a cone is increasing at a rate of
10
10
10
meters per second.
\newline
The height of the cone is fixed at
6
6
6
meters.
\newline
At a certain instant, the radius is
1
1
1
meter.
\newline
What is the rate of change of the volume of the cone at that instant (in cubic meters per second)?
\newline
Choose
1
1
1
answer:
\newline
(A)
40
π
40 \pi
40
π
\newline
(B)
200
π
200 \pi
200
π
\newline
(C)
400
π
400 \pi
400
π
\newline
(D)
20
π
20 \pi
20
π
\newline
The volume of a cone with radius
r
r
r
and height
h
h
h
is
π
r
2
h
3
\pi r^{2} \frac{h}{3}
π
r
2
3
h
.
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The surface area of a cube is increasing at a rate of
15
15
15
square meters per hour.
\newline
At a certain instant, the surface area is
24
24
24
square meters.
\newline
What is the rate of change of the volume of the cube at that instant (in cubic meters per hour)?
\newline
Choose
1
1
1
answer:
\newline
(A)
8
8
8
\newline
(B)
15
2
\frac{15}{2}
2
15
\newline
(C)
(
15
)
3
(\sqrt{15})^{3}
(
15
)
3
\newline
(D)
5
8
\frac{5}{8}
8
5
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The volume of a cube is increasing at a rate of
18
18
18
cubic meters per hour.
\newline
At a certain instant, the volume is
8
8
8
cubic meters.
\newline
What is the rate of change of the surface area of the cube at that instant (in square meters per hour)?
\newline
Choose
1
1
1
answer:
\newline
(A)
(
18
3
)
2
(\sqrt[3]{18})^{2}
(
3
18
)
2
\newline
(B)
36
36
36
\newline
(C)
3
2
\frac{3}{2}
2
3
\newline
(D)
24
24
24
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The side of the base of a square prism is increasing at a rate of
5
5
5
meters per second and the height of the prism is decreasing at a rate of
2
2
2
meters per second.
\newline
At a certain instant, the base's side is
6
6
6
meters and the height is
7
7
7
meters.
\newline
What is the rate of change of the volume of the prism at that instant (in cubic meters per second)?
\newline
Choose
1
1
1
answer:
\newline
(A)
492
492
492
\newline
(B)
−
492
-492
−
492
\newline
(C)
−
348
-348
−
348
\newline
(D)
348
348
348
\newline
The volume of a square prism with base side
s
s
s
and height
h
h
h
is
s
2
h
s^{2} h
s
2
h
.
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The radius of the base of a cone is increasing at a rate of
10
10
10
meters per second.
\newline
The height of the cone is fixed at
6
6
6
meters.
\newline
At a certain instant, the radius is
1
1
1
meter.
\newline
What is the rate of change of the volume of the cone at that instant (in cubic meters per second)?
\newline
Choose
1
1
1
answer:
\newline
(A)
20
π
20 \pi
20
π
\newline
(B)
40
π
40 \pi
40
π
\newline
(C)
400
π
400 \pi
400
π
\newline
(D)
200
π
200 \pi
200
π
\newline
The volume of a cone with radius
r
r
r
and height
h
h
h
is
π
r
2
h
3
\pi r^{2} \frac{h}{3}
π
r
2
3
h
.
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The surface area of a cylinder is increasing at a rate of
9
π
9 \pi
9
π
square meters per hour.
\newline
The height of the cylinder is fixed at
3
3
3
meters.
\newline
At a certain instant, the surface area is
36
π
36 \pi
36
π
square meters.
\newline
What is the rate of change of the volume of the cylinder at that instant (in cubic meters per hour)?
\newline
Choose
1
1
1
answer:
\newline
(A)
9
π
9 \pi
9
π
\newline
(B)
27
π
27 \pi
27
π
\newline
(C)
π
3
\frac{\pi}{3}
3
π
\newline
(D)
1
2
\frac{1}{2}
2
1
\newline
The surface area of a cylinder with base radius
r
r
r
and height
h
h
h
is
2
π
r
2
+
2
π
r
h
2 \pi r^{2}+2 \pi r h
2
π
r
2
+
2
π
r
h
.
\newline
The volume of a cylinder with base radius
r
r
r
and height
h
h
h
is
π
r
2
h
\pi r^{2} h
π
r
2
h
.
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Question
\newline
Find the volume and surface area of the following rectangular prism.
\newline
volume:
\newline
□
\square
□
\newline
Surface Area:
\newline
□
\square
□
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A sphere has a radius of
7
7
7
.
5
5
5
centimeters
(
c
m
)
(\mathrm{cm})
(
cm
)
.
\newline
Question:
\newline
To the nearest cubic centimeter, what is the volume of the sphere?
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Question
3
3
3
/
14
14
14
\newline
a
v
a^{v}
a
v
\newline
3
3
3
Find the volume and surface area of the following rectangular prism.
\newline
volume:
\newline
Surface Área:
□
\square
□
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Question
3
/
14
3 / 14
3/14
\newline
NEXT
\newline
BOOKMARK
\newline
4
4
4
\newline
3
3
3
Find the volume and surface area of the following rectangular prism.
\newline
Volume:
□
\square
□
\newline
Surface Area:
□
\square
□
Get tutor help
Question
3
3
3
/
14
14
14
\newline
pear Assessment
\newline
Desmosi Testing
\newline
d
43243
43243
43243
a
9100088
9100088
9100088
a
5190
5190
5190
/class/
64
64
64
ed
209
209
209
e
3
3
3
f
907876925
907876925
907876925
\newline
c
\newline
NEXT
\newline
BOOKMARK
\newline
3
3
3
Find the volume and surface area of the following rectangular prism.
\newline
volume:
□
\square
□
\newline
Surface Área:
□
\square
□
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Question
3
3
3
/
14
14
14
\newline
NEXT
\newline
BOOKMARK
\newline
3
3
3
Find the volume and surface area of the following rectangular prism.
\newline
volume:
□
\square
□
\newline
Surface Área:
□
\square
□
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Name
\qquad
-
\newline
138
=
138=
138
=
\newline
-
\newline
%
\%
%
Date
\qquad
\newline
Chapter
\newline
Test
\newline
Find the area of the figure.
\newline
1
1
1
.
\newline
11
11
11
\newline
3
3
3
.
\newline
5
5
5
. A worker charges
$
80
\$ 80
$80
per square foot to install windows. How much does it cost to install the window shown?
\newline
6
6
6
. Find the height of the triangle.
\newline
7
7
7
. Find the height of the trapezoid.
\newline
8
8
8
. The total area of the trapezoid is
102
102
102
square feet. What is the value of
x
x
x
?
\newline
9
9
9
. Find the number of faces, edges, and vertices of a triangular pyramid.
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6
6
6
. Write and simplify an expression for the volume of a rectangular prism with length
7.5
f
t
7.5 \mathrm{ft}
7.5
ft
, width
w
t
\mathrm{wt}
wt
, and height
4.2
f
t
4.2 \mathrm{ft}
4.2
ft
. What is the volume if the width is
2
f
t
2 \mathrm{ft}
2
ft
?
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5
5
5
. A right solid and its base are shown to the right. Find the volume of the solid given that its height is
3
3
3
inches. Dimensions are in inches.
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3
3
3
. Earl of March has been fundraising to build a running track in the sports field. The dimensions for this track are shown below.
\newline
a. Determine the perimeter around the outside of the track.
\newline
b. Determine the amount of space taken up by the actual track surface (not the interior of the track).
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A florist orders exactly
1
3
\frac{1}{3}
3
1
gallons of nutrient-rich water for each bushel of flowers he buys. The florist buys bushels of flowers at
$
1.20
\$ 1.20
$1.20
per bushel and gallons of nutrient-rich water at
$
0.60
\$ 0.60
$0.60
per gallon. Which of the following equations gives the total cost,
C
(
b
)
C(b)
C
(
b
)
, in dollars, for
b
b
b
bushels of flowers and the nutrient-rich water ordered for them?
\newline
Choose
1
1
1
answer:
\newline
(A)
C
(
b
)
=
(
1.2
+
0.2
)
⋅
b
C(b)=(1.2+0.2) \cdot b
C
(
b
)
=
(
1.2
+
0.2
)
⋅
b
\newline
(B)
C
(
b
)
=
3
⋅
0.6
⋅
b
C(b)=3 \cdot 0.6 \cdot b
C
(
b
)
=
3
⋅
0.6
⋅
b
\newline
(c)
C
(
b
)
=
(
1.2
+
0.6
)
⋅
b
C(b)=(1.2+0.6) \cdot b
C
(
b
)
=
(
1.2
+
0.6
)
⋅
b
\newline
(D)
C
(
b
)
=
7
⋅
0.6
⋅
b
C(b)=7 \cdot 0.6 \cdot b
C
(
b
)
=
7
⋅
0.6
⋅
b
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The volume of the cylinder is approximately I
97
97
97
.
9
9
9
cubic meters. What is the best estimate for the height of the cylinder? (Note:
\newline
The cylinder is not drawn to scale.)
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15
15
15
\newline
Earl is making a mold for creating cone-shaped candles. He starts with a cylindrical piece of wood and carves out a cone-shaped section. What is the approximate volume of the solid portion of the mold? Use
3
3
3
.
14
14
14
for pi.
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1
2
3
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4
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