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## Arcs and Sectors - Sample Math Practice Problems

The math problems below can be generated by MathScore.com, a math practice program for schools and individual families. References to complexity and mode refer to the overall difficulty of the problems as they appear in the main program. In the main program, all problems are automatically graded and the difficulty adapts dynamically based on performance. Answers to these sample questions appear at the bottom of the page. This page does not grade your responses.

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### Complexity=1, Mode=arc

Find the length of the arc in terms of pi.
Type "pi" in for π. Example: "7π m2" as "7pi sq m".

 1.   The radius of the circle is 3 in. Length = 2.   The radius of the circle is 8 km. Length =

### Complexity=1, Mode=sect

Find the area of the sector in terms of pi.
Type "pi" in for π. Example: "7π m2" as "7pi sq m".

 1.   The radius of the circle is 4 cm. Area = 2.   The radius of the circle is 2 in. Area =

### Complexity=2, Mode=arc

Find the length of the highlighted arc (red) in terms of pi.
Type "pi" in for π. Example: "7π m2" as "7pi sq m".

 1.   The radius of the circle is 10 ft. Length = 2.   The radius of the circle is 10 mm. Length =

### Complexity=2, Mode=sect

Find the area of the sector in terms of pi.
Type "pi" in for π. Example: "7π m2" as "7pi sq m".

 1.   The radius of the circle is 2 m. Area = 2.   The radius of the circle is 5 cm. Area =

### Complexity=3, Mode=ang

Solve.

 1.   An arc has a length of 20/3 π cm and a radius of 6 cm. Calculate the angle of the arc. ° 2.   What is the measure of the central angle of a sectorif its area is 75/4 π ft2 and its radius is 5 ft? °

## Answers

### Complexity=1, Mode=arc

Find the length of the arc in terms of pi.
Type "pi" in for π. Example: "7π m2" as "7pi sq m".

#ProblemCorrect AnswerYour Answer
1
The radius of the circle is 3 in.
Length =
Solution
Arc length = central angle
360°
circumference
=
 36360
2π(3 in)
=
 110
6π in
=
 6π10
in
Answer is
 35
π  in.
#ProblemCorrect AnswerYour Answer
2
The radius of the circle is 8 km.
Length =
Solution
Arc length = central angle
360°
circumference
=
 54360
2π(8 km)
=
 320
16π km
=
 3 • 16π20
km
Answer is
 125
π  km.

### Complexity=1, Mode=sect

Find the area of the sector in terms of pi.
Type "pi" in for π. Example: "7π m2" as "7pi sq m".

#ProblemCorrect AnswerYour Answer
1
The radius of the circle is 4 cm.
Area =
Solution
Sector area = central angle
360°
circle area
=
 63360
π(4 cm)2
=
 740
16π cm2
=
 7 • 16π40
cm2
Answer is
 145
π  cm2.
#ProblemCorrect AnswerYour Answer
2
The radius of the circle is 2 in.
Area =
Solution
Sector area = central angle
360°
circle area
=
 320360
π(2 in)2
=
 89
4π in2
=
 8 • 4π9
in2
Answer is
 329
π  in2.

### Complexity=2, Mode=arc

Find the length of the highlighted arc (red) in terms of pi.
Type "pi" in for π. Example: "7π m2" as "7pi sq m".

#ProblemCorrect AnswerYour Answer
1
The radius of the circle is 10 ft.
Length =
Solution
Arc length = central angle
360°
circumference

= 360° - 297°
360°
2π(10 ft)

=
 63360
2π(10 ft)
=
 740
20π ft
=
 7 • 20π40
ft
Answer is
 72
π  ft.
#ProblemCorrect AnswerYour Answer
2
The radius of the circle is 10 mm.
Length =
Solution
Arc length = central angle
360°
circumference

= 360° - 306°
360°
2π(10 mm)

=
 54360
2π(10 mm)
=
 320
20π mm
=
 3 • 20π20
mm
 Answer is 3 π mm.

### Complexity=2, Mode=sect

Find the area of the sector in terms of pi.
Type "pi" in for π. Example: "7π m2" as "7pi sq m".

#ProblemCorrect AnswerYour Answer
1
The radius of the circle is 2 m.
Area =
Solution
Sector area = central angle
360°
circle area

= 360° - 160°
360°
π(2 m)2

=
 200360
π(2 m)2
=
 59
4π m2
=
 5 • 4π9
m2
Answer is
 209
π  m2.
#ProblemCorrect AnswerYour Answer
2
The radius of the circle is 5 cm.
Area =
Solution
Sector area = central angle
360°
circle area

= 360° - 40°
360°
π(5 cm)2

=
 320360
π(5 cm)2
=
 89
25π cm2
=
 8 • 25π9
cm2
Answer is
 2009
π  cm2.

### Complexity=3, Mode=ang

Solve.

#ProblemCorrect AnswerYour Answer
1An arc has a length of 20/3 π cm and a radius of 6 cm.
Calculate the angle of the arc.
°
Solution
 Arc length = central angle360° • Circumference

 central angle = Arc length • 360°2πr = 20/3 π cm • 360°12π cm
The answer is 200°.
#ProblemCorrect AnswerYour Answer
2What is the measure of the central angle of a sector
if its area is 75/4 π ft2 and its radius is 5 ft?
°
Solution
 Asector = central angle360° • Acircle

 central angle = Asector • 360°πr2 = 75/4 π ft2 • 360°25π ft2
The answer is 270°.
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