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Math Problems
Algebra 2
Find the radius or diameter of a circle
4
4
4
. Determine the dimensions of a rectangular solid with a square base of maximum volume if its surface area is
150
150
150
square inches.
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A circle in the
x
y
xy
x
y
-plane has the equation
x
2
+
y
2
+
a
x
+
b
y
+
c
=
0
x^2 + y^2 + ax + by + c = 0
x
2
+
y
2
+
a
x
+
b
y
+
c
=
0
. What is the center of the circle?
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What is the side length of a square that has an area of
144
f
t
2
144 \mathrm{ft}^{2}
144
ft
2
?
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Find the volume of a hemisphere with a great circle circumference of
37.7
37.7
37.7
centimeters.
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Find the center and the radius of the circle. Then graph the circle.
\newline
(
x
+
3
)
2
+
(
y
−
1
)
2
=
16
(x+3)^{2}+(y-1)^{2}=16
(
x
+
3
)
2
+
(
y
−
1
)
2
=
16
\newline
Use the graphing tool to graph the circle.
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An engineer is planning a new water pipe installation. The circular pipe has a diameter of
d
=
20
c
m
d=20 \mathrm{~cm}
d
=
20
cm
.
\newline
What is the area
A
A
A
of the circular cross section of this pipe?
\newline
Give your answer in terms of pi.
\newline
A
=
□
A=\square
A
=
□
c
m
2
cm^{2}
c
m
2
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A building engineer analyzes a concrete column with a circular cross section. The circumference of the column is
18
π
18 \pi
18
π
meters.
\newline
What is the area
A
A
A
of the cross section of the column?
\newline
Give your answer in terms of pi.
\newline
A
=
□
A=\square
A
=
□
m
2
\mathrm{m}^{2}
m
2
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Q. Find the radius of circle whose area is
616
c
m
2
616 \mathrm{~cm}^{2}
616
cm
2
.
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What is the surface area of the prism having the base area
25
m
2
25 \, \text{m}^2
25
m
2
, base perimeter
24
m
24 \, \text{m}
24
m
and length
12
m
12\,\text{m}
12
m
?
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Find the volume of the given solid.
\newline
bounded by the planes
z
=
x
,
y
=
x
,
x
+
y
=
9
z=x, y=x, x+y=9
z
=
x
,
y
=
x
,
x
+
y
=
9
and
z
=
0
z=0
z
=
0
\newline
□
\square
□
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Check the position of the Point
(
5
,
6
)
(5,6)
(
5
,
6
)
with respect to its circle
2
x
2
+
2
y
2
+
12
x
−
8
y
+
1
=
0
2x^2+2y^2+12x-8y+1=0
2
x
2
+
2
y
2
+
12
x
−
8
y
+
1
=
0
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Circle
O
O
O
shown below has a radius of
25
25
25
inches. Find, to the nearest tenth, the radian measure of the angle,
x
x
x
, that forms an arc whose length is
18
18
18
inches.
\newline
Answer:
□
\square
□
radians
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Circle
O
O
O
shown below has a radius of
8
8
8
inches. Find, to the nearest tenth, the radian measure of the angle,
x
x
x
, that forms an arc whose length is
12
12
12
inches.
\newline
Answer:
□
\square
□
radians
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Circle
O
O
O
shown below has a radius of
20
20
20
inches. Find, to the nearest tenth, the radian measure of the angle,
x
x
x
, that forms an arc whose length is
40
40
40
inches.
\newline
Answer:
□
\square
□
radians
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Circle
O
O
O
shown below has a radius of
11
11
11
inches. Find, to the nearest tenth, the radian measure of the angle,
x
x
x
, that forms an arc whose length is
26
26
26
inches.
\newline
Answer:
□
\square
□
radians
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find the arc length of a sector if the radius is
5
cm
5\,\text{cm}
5
cm
and the area of the sector is
74.5
74.5
74.5
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Avery is designing a large rectangular sign. They want the sign to have an area of
A
A
A
and a width of
w
w
w
. How tall should the sign be?
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What is the surface area of the cylinder height
5
5
5
and radius
4
4
4
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What is the surface area of a cone with a lateral height of
10
10
10
inches, a diameter of
12
12
12
inches, and a height of
8
8
8
inches
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The circle with radius
3
3
3
has a sector with a central angle of
160
160
160
degrees. What is the area of the sector?
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Select the type of cross section formed when a right cylinder is cut parallel to its base.
\newline
square
\newline
pentagon
\newline
Submit Answer
\newline
circle
\newline
rectangle
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A manufacturer has
200
m
2
200m^{2}
200
m
2
of sheet metal. What are the dimensions of the cylindrical tank of maximum volume that can be produced using this amount of sheet metal?
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A circle has a circumference of
50
50
50
.
24
24
24
units.
\newline
What is the radius of the circle?
\newline
Use
3
3
3
.
14
14
14
for
π
\pi
π
and enter your answer as a decimal.
\newline
□
\square
□
units
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A cone and sphere have equal volumes and radii of equal length. If the height of the cone is
36
36
36
centimeters, then what is the length of the radius of each shape in centimeters?
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A circle in the
x
y
x y
x
y
-plane has the equation
4
x
2
+
4
y
2
−
24
x
=
28
4 x^{2}+4 y^{2}-24 x=28
4
x
2
+
4
y
2
−
24
x
=
28
. What is the diameter of the circle?
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A circle in the
x
y
x y
x
y
-plane has the equation
\newline
(
x
−
0.8
)
2
+
(
y
−
5.2
)
2
=
1.69
.
(x-0.8)^{2}+(y-5.2)^{2}=1.69 \text {. }
(
x
−
0.8
)
2
+
(
y
−
5.2
)
2
=
1.69
.
\newline
How long is the radius of the circle?
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A circle in the
x
y
x y
x
y
-plane has its center at the point
(
−
6
,
1
)
(-6,1)
(
−
6
,
1
)
. If the point
(
7
,
12
)
(7,12)
(
7
,
12
)
lies on the circle, what is the radius of the circle?
\newline
(Round the answer to the nearest integer.)
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A circle has a circumference of
12
π
12 \pi
12
π
feet
(
f
t
)
(\mathrm{ft})
(
ft
)
. An arc,
x
x
x
, in this circle has a central angle of
33
0
∘
330^{\circ}
33
0
∘
. Rounded to the nearest foot, what is the length of
x
x
x
?
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A circle has a circumference of
6
π
6 \pi
6
π
feet
(
f
t
)
(\mathrm{ft})
(
ft
)
. An arc,
x
x
x
, in this circle has a central angle of
5
0
∘
50^{\circ}
5
0
∘
. Rounded to the nearest tenth of a foot, what is the length of
x
x
x
?
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What is the radius of the circle
x
2
+
y
2
=
36
x^2 + y^2 = 36
x
2
+
y
2
=
36
?
\newline
Simplify any fractions.
\newline
____
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