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Math Problems
Grade 8
Circles: word problems
Lateral Surface Area (LSA) of a Triangular Prism
\newline
L
S
A
=
(
S
1
+
S
2
+
b
)
×
1
L S A=\left(S_{1}+S_{2}+b\right) \times 1
L
S
A
=
(
S
1
+
S
2
+
b
)
×
1
\newline
here,
\newline
S
1
,
S
2
S_{1}, S_{2}
S
1
,
S
2
and
b
=
b=
b
=
egdes of the base I = length of the prism
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Penalty: none
\newline
Question
\newline
Watch Video
\newline
Show Examples
\newline
Nasim is flying a kite, holding his nce of
2
2
2
.
5
5
5
feet above the ground and letting all the kite's string play out. He measuic ur elevation from his hand to the kite to be
28
28
28
If the string from the kite to his hand is
105
105
105
feet long, how many feet is the kite above the ground? Round your answer to the nearest hundredth of a foot if necessary.
\newline
Answer Attempt
1
1
1
out of
2
2
2
\newline
□
\square
□
feet
\newline
Submit Answer
\newline
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2024
2024
2024
DeltaMathcom, All Rights Reserved. Privacy Policyl Terms of Service
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centimeters. Find the radius.
\newline
ches. Find the diameter.
\newline
(Sect
\newline
gure. (Section
8
8
8
.
2
2
2
)
\newline
4
4
4
.
\newline
circle. Use
3
3
3
.
14
14
14
or
22
7
\frac{22}{7}
7
22
for
π
\pi
π
\newline
Section
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centimeters. Find the radius.
\newline
iches. Find the diameter.
\newline
(Sect
\newline
gure. (Section
8
8
8
.
2
2
2
)
\newline
4
4
4
.
\newline
circle. Use
3.14
3.14
3.14
or
\newline
(
22
)
/
(
7
)
(22)/(7)
(
22
)
/
(
7
)
for
\newline
π
\pi
π
\newline
Section
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ry Period
323
323
323
.
24
24
24
\newline
DeltaMath Student Application
\newline
New Tab
\newline
676
/
22950809
/
6
b
525
f
7
676 / 22950809 / 6 b 525 f 7
676/22950809/6
b
525
f
7
debe
67
67
67
ceec
45
45
45
cb
3
3
3
b
51
51
51
fb
7
7
7
c
6
6
6
b
9
9
9
\newline
Biology
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ehallpass
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ALEKS - Adaptive L..
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Mr Caert
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iBlocks Online - Proj..
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All
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Watch Video
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Show Examples
\newline
Question
\newline
(
2
2
2
) Watch Video
\newline
Show Examples
\newline
Find the volume of a pyramid with a square base, where the side length of the base is
14
14
14
.
7
7
7
in and the height of the pyramid is
17
17
17
.
2
2
2
in. Round your answer to the nearest tenth of a cubic inch.
\newline
Answer Attempt
2
2
2
out of
2
2
2
\newline
Still Stuc
\newline
in
3
^{3}
3
\newline
Submit Answer
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Find the area of each shaded sector. Use
3
3
3
.
14
14
14
for
p
l
\mathrm{pl}
pl
and round to the nearest tenth.
\newline
12
12
12
.
\newline
13
13
13
.
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The diameter of a circle is
14
14
14
yards. What is the circle's circumference?
\newline
Use
π
≈
3.14
\pi \approx 3.14
π
≈
3.14
and round your answer to the nearest hundredth.
\newline
yards
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Two observers are
500
f
t
500 \mathrm{ft}
500
ft
apart on opposite sides of a flagpole. The angles of elevation from the observers to the top of the pole are
1
8
∘
18^{\circ}
1
8
∘
and
2
0
∘
20^{\circ}
2
0
∘
. Find the height of the flagpole.
\newline
The flagpole is
□
\square
□
ft righ.
\newline
(Round to the nearest tenth as needed.)
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A monkey is swinging from a tree. On the first swing, she passes through an arc of
20
m
20 \mathrm{~m}
20
m
. With each swing, she passes through an arc
4
5
\frac{4}{5}
5
4
the length of the previous swing.
\newline
What is the total distance the monkey has traveled when she completes her
1
0
th
10^{\text {th }}
1
0
th
swing?
\newline
Round your final answer to the nearest meter.
\newline
□
\square
□
m
\mathrm{m}
m
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A monkey is swinging from a tree. On the first swing, she passes through an arc of
10
m
10 \mathrm{~m}
10
m
. With each swing, she passes through an arc
9
10
\frac{9}{10}
10
9
the length of the previous swing.
\newline
What is the total distance the monkey has traveled when she completes her
2
5
th
25^{\text {th }}
2
5
th
swing?
\newline
Round your final answer to the nearest meter.
\newline
□
\square
□
m
\mathrm{m}
m
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Cecelia went on a hiking trip. The first day she walked
27
27
27
kilometers. Each day since, she walked
2
3
\frac{2}{3}
3
2
of what she walked the day before.
\newline
What is the total distance Cecelia has traveled by the end of the
5
th
5^{\text {th }}
5
th
day?
\newline
Round your final answer to the nearest kilometer.
\newline
□
\square
□
k
m
\mathrm{km}
km
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The area of a circle is
9
π
9 \pi
9
π
square kilometers. What is the radius?
\newline
Give the exact answer in simplest form.
\newline
□
\square
□
kilometers
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Harper uploaded a funny video of her dog onto a website.
\newline
The relationship between the elapsed time,
d
d
d
, in days, since the video was first uploaded, and the total number of views,
V
(
d
)
V(d)
V
(
d
)
, that the video received is modeled by the following function.
\newline
V
(
d
)
=
4
1.25
d
V(d)=4^{1.25 d}
V
(
d
)
=
4
1.25
d
\newline
How many views will the video receive after
6
6
6
days?
\newline
Round your answer, if necessary, to the nearest hundredth.
\newline
□
\square
□
views
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find the volume of a pyramid with a square base, where the area of the base is the
16
×
16
m
2
16\times16\,\text{m}^2
16
×
16
m
2
and the height of the pyramid is
25.4
mm
25.4\,\text{mm}
25.4
mm
. round your answer to the nearest tenth of a cubic meter
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A shipping container is in the form of a right rectangular prism and it can hold
2310
2310
2310
cubic feet of shipped goods when it is full. Its length is
35
f
t
35 \mathrm{ft}
35
ft
and its height is
8
f
t
3
8 \mathrm{ft} 3
8
ft
3
inches. Find the width of the container in feet. Round your answer to the nearest tenth if necessary.
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Question
\newline
Watch Video
\newline
In circle
W
,
m
∠
V
W
X
=
11
9
∘
W, \mathrm{~m} \angle V W X=119^{\circ}
W
,
m
∠
VW
X
=
11
9
∘
. Solve for
x
x
x
if
m
V
X
=
(
12
x
+
27
)
∘
\mathrm{m} V X=(12 x+27)^{\circ}
m
V
X
=
(
12
x
+
27
)
∘
. If necessary, round your answer to the nearest tenth.
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Circle
O
O
O
shown below has a radius of
7
7
7
inches. To the nearest tenth of an inch, determine the length of the arc,
x
x
x
, subtended by an angle of
1
1
1
.
4
4
4
radians.
\newline
Answer:
□
\square
□
inches
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Circle
O
O
O
shown below has an arc of length
29
29
29
inches subtended by an angle of
1
1
1
.
1
1
1
radians. Find the length of the radius,
x
x
x
, to the nearest tenth of an inch.
\newline
Answer:
□
\square
□
inches
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Circle
O
O
O
shown below has an arc of length
19
19
19
inches subtended by an angle of
1
1
1
radians. Find the length of the radius,
x
x
x
, to the nearest tenth of an inch.
\newline
Answer:
□
\square
□
inches
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Circle
O
O
O
shown below has a radius of
3
3
3
inches. To the nearest tenth of an inch, determine the length of the arc,
x
x
x
, subtended by an angle of
7
0
∘
70^{\circ}
7
0
∘
.
\newline
Answer:
□
\square
□
inches
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Circle
O
O
O
shown below has an arc of length
3
3
3
inches subtended by an angle of
1
1
1
.
5
5
5
radians. Find the length of the radius,
x
x
x
, to the nearest tenth of an inch.
\newline
Answer:
□
\square
□
inches
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Circle
O
O
O
shown below has a radius of
4
4
4
inches. Find, to the nearest tenth of a degree, the measure of the angle,
x
x
x
, that forms an arc whose length is
7
7
7
inches.
\newline
Answer:
□
∘
\square^{\circ}
□
∘
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Circle
O
O
O
shown below has a radius of
3
3
3
inches. Find, to the nearest tenth of a degree, the measure of the angle,
x
x
x
, that forms an arc whose length is
4
4
4
inches.
\newline
Answer:
□
∘
\square^{\circ}
□
∘
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Circle
O
O
O
shown below has a radius of
11
11
11
inches. Find, to the nearest tenth of
a
a
a
degree, the measure of the angle,
x
x
x
, that forms an arc whose length is
24
24
24
inches.
\newline
Answer:
□
∘
\square^{\circ}
□
∘
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Circle
O
O
O
shown below has an arc of length
46
46
46
inches subtended by an angle of
13
6
∘
136^{\circ}
13
6
∘
.
\newline
Find the length of the radius,
x
x
x
, to the nearest tenth of an inch.
\newline
Answer:
□
\square
□
inches
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Circle
O
O
O
shown below has a radius of
25
25
25
inches. To the nearest tenth of an inch, determine the length of the arc,
x
x
x
, subtended by an angle of
2
2
2
.
2
2
2
radians.
\newline
Answer:
□
\square
□
inches
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Circle
O
O
O
shown below has an arc of length
5
5
5
inches subtended by an angle of
10
3
∘
103^{\circ}
10
3
∘
.
\newline
Find the length of the radius,
x
x
x
, to the nearest tenth of an inch.
\newline
Answer:
□
\square
□
inches
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Circle
O
O
O
shown below has an arc of length
57
57
57
inches subtended by an angle of
10
6
∘
106^{\circ}
10
6
∘
.
\newline
Find the length of the radius,
x
x
x
, to the nearest tenth of an inch.
\newline
Answer:
□
\square
□
inches
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Circle
O
O
O
shown below has a radius of
13
13
13
inches. To the nearest tenth of an inch, determine the length of the arc,
x
x
x
, subtended by an angle of
0
0
0
.
9
9
9
radians.
\newline
Answer:
□
\square
□
inches
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Circle
O
O
O
shown below has an arc of length
48
48
48
inches subtended by an angle of
1
1
1
.
6
6
6
radians. Find the length of the radius,
x
x
x
, to the nearest tenth of an inch.
\newline
Answer:
□
\square
□
inches
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Circle
O
O
O
shown below has a radius of
27
27
27
inches. To the nearest tenth of an inch, determine the length of the arc,
x
x
x
, subtended by an angle of
1
1
1
.
2
2
2
radians.
\newline
Answer:
□
\square
□
inches
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In
△
U
V
W
,
w
=
8.9
\triangle \mathrm{UVW}, w=8.9
△
UVW
,
w
=
8.9
inches,
v
=
9
v=9
v
=
9
inches and
∠
V
=
5
0
∘
\angle \mathrm{V}=50^{\circ}
∠
V
=
5
0
∘
. Find all possible values of
∠
W
\angle \mathrm{W}
∠
W
, to the nearest
10
10
10
th of a degree.
\newline
Answer:
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In
△
W
X
Y
,
y
=
1.3
\triangle \mathrm{WXY}, y=1.3
△
WXY
,
y
=
1.3
inches,
x
=
1.1
x=1.1
x
=
1.1
inches and
∠
X
=
5
1
∘
\angle \mathrm{X}=51^{\circ}
∠
X
=
5
1
∘
. Find all possible values of
∠
Y
\angle \mathrm{Y}
∠
Y
, to the nearest
10
10
10
th of a degree.
\newline
Answer:
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The actual dimensions of a rectangle are
6
6
6
in by
9
9
9
in. Eric measures the sides to be
5
5
5
.
96
96
96
in by
8
8
8
.
75
75
75
in. In calculating the area, what is the relative error, to the nearest hundredth.
\newline
Answer:
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The volume of a rectangular prism is
441
c
m
3
441 \mathrm{~cm}^{3}
441
cm
3
. Alex measures the sides to be
6.6
c
m
6.6 \mathrm{~cm}
6.6
cm
by
6.93
c
m
6.93 \mathrm{~cm}
6.93
cm
by
8.51
c
m
8.51 \mathrm{~cm}
8.51
cm
. In calculating the volume, what is the relative error, to the nearest hundredth.
\newline
Answer:
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The volume of a rectangular prism is
336
c
m
3
336 \mathrm{~cm}^{3}
336
cm
3
. Eric measures the sides to be
6.34
c
m
6.34 \mathrm{~cm}
6.34
cm
by
8.03
c
m
8.03 \mathrm{~cm}
8.03
cm
by
7.46
c
m
7.46 \mathrm{~cm}
7.46
cm
. In calculating the volume, what is the relative error, to the nearest thousandth.
\newline
Answer:
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The volume of a rectangular prism is
720
f
t
3
720 \mathrm{ft}^{3}
720
ft
3
. Alex measures the sides to be
9.66
f
t
9.66 \mathrm{ft}
9.66
ft
by
9.11
f
t
9.11 \mathrm{ft}
9.11
ft
by
7.59
f
t
7.59 \mathrm{ft}
7.59
ft
. In calculating the volume, what is the relative error, to the nearest thousandth.
\newline
Answer:
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The volume of a rectangular prism is
63
f
t
3
63 \mathrm{ft}^{3}
63
ft
3
. Eric measures the sides to be
6.59
f
t
6.59 \mathrm{ft}
6.59
ft
by
3.44
f
t
3.44 \mathrm{ft}
3.44
ft
by
3.15
f
t
3.15 \mathrm{ft}
3.15
ft
. In calculating the volume, what is the relative error, to the nearest thousandth.
\newline
Answer:
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The volume of a rectangular prism is
480
c
m
3
480 \mathrm{~cm}^{3}
480
cm
3
. David measures the sides to be
6
6
6
.
49
49
49
c
m
\mathrm{cm}
cm
by
9.99
c
m
9.99 \mathrm{~cm}
9.99
cm
by
8.41
c
m
8.41 \mathrm{~cm}
8.41
cm
. In calculating the volume, what is the relative error, to the nearest hundredth.
\newline
Answer:
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The volume of a rectangular prism is
300
i
n
3
300 \mathrm{in}^{3}
300
in
3
. David measures the sides to be
2
2
2
.
8
8
8
in by
10
10
10
.
35
35
35
in by
9.9
i
n
9.9 \mathrm{in}
9.9
in
. In calculating the volume, what is the relative error, to the nearest thousandth.
\newline
Answer:
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The volume of a rectangular prism is
126
f
t
3
126 \mathrm{ft}^{3}
126
ft
3
. Bob measures the sides to be
9.48
f
t
9.48 \mathrm{ft}
9.48
ft
by
7.21
f
t
7.21 \mathrm{ft}
7.21
ft
by
1.93
f
t
1.93 \mathrm{ft}
1.93
ft
. In calculating the volume, what is the relative error, to the nearest thousandth.
\newline
Answer:
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The volume of a rectangular prism is
140
f
t
3
140 \mathrm{ft}^{3}
140
ft
3
. Eric measures the sides to be
7.12
f
t
7.12 \mathrm{ft}
7.12
ft
by
3.83
f
t
3.83 \mathrm{ft}
3.83
ft
by
5.49
f
t
5.49 \mathrm{ft}
5.49
ft
. In calculating the volume, what is the relative error, to the nearest thousandth.
\newline
Answer:
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The volume of a rectangular prism is
270
i
n
3
270 \mathrm{in}^{3}
270
in
3
. Alex measures the sides to be
5
5
5
.
71
71
71
in by
5
5
5
.
46
46
46
in by
9
9
9
.
4
4
4
in. In calculating the volume, what is the relative error, to the nearest hundredth.
\newline
Answer:
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The volume of a rectangular prism is
48
c
m
3
48 \mathrm{~cm}^{3}
48
cm
3
. David measures the sides to be
6.1
c
m
6.1 \mathrm{~cm}
6.1
cm
by
3.89
c
m
3.89 \mathrm{~cm}
3.89
cm
by
2.21
c
m
2.21 \mathrm{~cm}
2.21
cm
. In calculating the volume, what is the relative error, to the nearest hundredth.
\newline
Answer:
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The volume of a rectangular prism is
108
c
m
3
108 \mathrm{~cm}^{3}
108
cm
3
. Eric measures the sides to be
3.32
c
m
3.32 \mathrm{~cm}
3.32
cm
by
4.04
c
m
4.04 \mathrm{~cm}
4.04
cm
by
8.72
c
m
8.72 \mathrm{~cm}
8.72
cm
. In calculating the volume, what is the relative error, to the nearest thousandth.
\newline
Answer:
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The earth’s radius is about
6370
km
6370\,\text{km}
6370
km
. Five to ten
km
\text{km}
km
above the surface of the earth, the gravitational force still equals
m
g
mg
m
g
. (
g
=
9.8
m/s
2
g = 9.8\,\text{m/s}^2
g
=
9.8
m/s
2
). That is still considered to be the surface of the earth. If you launch something parallel to the ground at the equator (a few
km
\text{km}
km
above the ground to avoid hitting a mountain), at what speed, the object will be able to orbit the earth instead of falling to the ground? Answer
m/s
\text{m/s}
m/s
or Answer
mile per hour
\text{mile per hour}
mile per hour
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A circle has a circumference of
12
π
12\pi
12
π
feet. An arc,
x
x
x
, in this circle has a central angle of
330
330
330
degrees. Rounded to the nearest foot, what is the length of
x
x
x
?
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Holtzman Clothiers's stock currently sells for
$
36.00
\$36.00
$36.00
a share. It just paid a dividend of
$
1.00
\$1.00
$1.00
a share (i.e.,
D
0
=
$
1.00
D_0 = \$1.00
D
0
=
$1.00
). The dividend is expected to grow at a constant rate of
9
%
9\%
9%
a year. What stock price is expected
1
1
1
year from now? Round your answer to the nearest cent.
$
\$
$
What is the required rate of return? Do not round intermediate calculations. Round your answer to two decimal places.
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A boat is heading towards a lighthouse, whose beacon-light is
111
111
111
feet above the water. From point
A
A
A
, the boat’s crew measures the angle of elevation to the beacon,
6
∘
6^\circ
6
∘
, before they draw closer. They measure the angle of elevation a second time from point
B
B
B
at some later time to be
1
3
∘
13^\circ
1
3
∘
. Find the distance from point
A
A
A
to point
B
B
B
. Round your answer to the nearest tenth of a foot if necessary.
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Andrew is pulling a sled with a force of
275
275
275
newtons by holding a rope at a
5
8
∘
58^{\circ}
5
8
∘
angle. His brother Austin is pushing the sled with a force of
320
320
320
newtons. Determine the magnitude and direction of the resultant force on the sled. Round all angles to the nearest tenth and sides to the nearest hundredths.
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