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Math Problems
Grade 8
Circles: word problems
You might need: Calculator Problem
\newline
You spin the spinner shown below once. Each sector shown has an equal area. What is \
P(shaded sector
)
\text{P(shaded sector})
P(shaded sector
)
? If necessary, round your answer to \\(2\) decimal places.
\newline
A)
0
0
0
.
25
25
25
\newline
B)
0
0
0
.
50
50
50
\newline
C)
0
0
0
.
75
75
75
\newline
D)
1
1
1
.
00
00
00
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The perimeter of a quarter circle is
17.85
17.85
17.85
millimeters. What is the quarter circle's radius?
P
=
17.85
P=17.85
P
=
17.85
mm Use
π
≈
3.14
\pi \approx 3.14
π
≈
3.14
and round your answer to the nearest hundredth.
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The perimeter of a quarter circle is
3.57
3.57
3.57
yards. What is the quarter circle's radius?
\newline
\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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The button on Camille's coat has a radius of
4
4
4
millimeters. What is the button's circumference?
\newline
Use
3.14
3.14
3.14
for
π
\pi
π
. If necessary, round your answer to the nearest hundredth.
\newline
_____ millimeters
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A circular bracelet has a radius of
3
centimeters
3\,\text{centimeters}
3
centimeters
. What is the bracelet's circumference?
\newline
Use
3.14
3.14
3.14
for
π
\pi
π
. If necessary, round your answer to the nearest hundredth.
\newline
_____ centimeters
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A subway token has a radius of
1
1
1
centimeter. What is the token's circumference?
\newline
Use
3.14
3.14
3.14
for
π
\pi
π
. If necessary, round your answer to the nearest hundredth.
\newline
_____ centimeters
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The Jones family has a circular vegetable garden beside their house. The garden has a radius of
15
15
15
yards. What is the area of the vegetable garden? Round your answer to the nearest hundredth of a square yard.
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A circle's circumference is
24
π
24 \pi
24
π
kilometers. What is its area?
\newline
Use
3.14
3.14
3.14
for
π
\pi
π
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The diameter of a circle is
6
6
6
Inches. What is the circumference?
\newline
Give the exact answer in simplest form.
\newline
□
\square
□
inches
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Find the
3
r
d
3^{\mathrm{rd}}
3
rd
partial sum of the series
∑
n
=
1
(
−
1
)
n
4
2
n
4
3
+
6
\sum_{n=1}(-1)^{n} \frac{4}{2 n^{\frac{4}{3}}+6}
∑
n
=
1
(
−
1
)
n
2
n
3
4
+
6
4
. Then use the alternating series error bound to find an upper and lower bound for the sum of the series. Round to three decimal places.
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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. What is the total distance Cecelia has traveled by the end of the
5
th
5^{\text{th}}
5
th
day? Round your final answer to the nearest kilometer.
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A cathedral has a large, circular stained-glass window. It has a diameter of
2
2
2
meters. What is the window's area?
\newline
Use
3.14
3.14
3.14
for
π
\pi
π
. If necessary, round your answer to the nearest hundredth.
\newline
_____ square meters
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A subway token has a radius of
1
1
1
centimeter. What is the token's area?
\newline
Use
3.14
3.14
3.14
for
π
\pi
π
. If necessary, round your answer to the nearest hundredth.
\newline
_____ square centimeters
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The button on Dustin's shirt has a diameter of
8
8
8
millimeters. What is the button's circumference?
\newline
Use
3.14
3.14
3.14
for
π
\pi
π
. If necessary, round your answer to the nearest hundredth.
\newline
_____ millimeters
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After stepping into a room with unusual lighting, Anita's pupil has a diameter of
6
6
6
millimeters. What is the pupil's area?
\newline
Use
3.14
3.14
3.14
for
π
\pi
π
. If necessary, round your answer to the nearest hundredth.
\newline
_____ square millimeters
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While running for class president, Estelle handed out a campaign button. The button has a radius of
4
4
4
centimeters. What is the button's area?
\newline
Use
3.14
3.14
3.14
for
π
\pi
π
. If necessary, round your answer to the nearest hundredth.
\newline
_____ square centimeters
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Norma works at a lab with a huge circular particle accelerator. It has a diameter of
4
4
4
miles. What is the accelerator's circumference?
\newline
Use
3.14
3.14
3.14
for
π
\pi
π
. If necessary, round your answer to the nearest hundredth.
\newline
_____ miles
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The lens of a telescope has a diameter of
8
8
8
feet. What is the lens's area?
\newline
Use
3.14
3.14
3.14
for
π
\pi
π
. If necessary, round your answer to the nearest hundredth.
\newline
_____ square feet
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As a contestant on a televised game show, Tori gets to spin the big prize wheel, which has a radius of
3
3
3
yards. What is the prize wheel's area?
\newline
Use
3.14
3.14
3.14
for
π
\pi
π
. If necessary, round your answer to the nearest hundredth.
\newline
_____ square yards
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A monkey is swinging from a tree. On the first swing, she passes through an arc of
20
m
20\text{m}
20
m
. With each swing, she passes through an arc
4
5
\frac{4}{5}
5
4
the length of the previous swing. What is the total distance the monkey has traveled when she completes her
1
0
th
10^{\text{th}}
1
0
th
swing? Round your final answer to the nearest meter.
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Wilber wants to make the pond in his backyard bigger. It is currently a cone with a radius of
30
30
30
meters and a depth of
15
15
15
meters. He wants to increase the radius to
40
40
40
meters and the depth to
20
20
20
meters. How much more water will the pond hold, in thousands of cubic meters?
\newline
(Round to the nearest thousand cubic meters.)
\newline
□
\square
□
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The diameter of a circle is
13
in
13\,\text{in}
13
in
. Find its area to the nearest whole number.
\newline
A
=
□
in
2
A=\square\,\text{in}^2
A
=
□
in
2
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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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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 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
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
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
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 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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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
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
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 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
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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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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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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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
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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