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Circles Practice Tests

These Grade 10 Geometry practice tests develop circle vocabulary, measurement formulas, arc and angle reasoning, chord and tangent theorems, sectors, and coordinate applications.

Skills covered

  • Identifying centers, radii, diameters, chords, secants, tangents, arcs, sectors, and central angles
  • Using circumference, area, arc length, sector area, radius, and diameter formulas
  • Applying central-angle, inscribed-angle, semicircle, tangent-radius, and chord theorems
  • Using chord-chord, tangent-secant, and secant-secant product relationships
  • Writing circle equations and solving coordinate, rotation, tire, map, and real-world measurement problems

How to use these practice tests

Start by identifying the circle part or theorem involved. Then decide whether the problem uses radius or diameter and whether an arc or sector is a fraction of the full circle.

For more Grade 10 Math practice, return to the Grade 10 Math category.

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5 Tests
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2. Test

Grade 10 Circles Practice Tests

Practice Grade 10 Geometry questions about circle vocabulary, circumference, area, arcs, angles, chords, tangents, secants, sectors, and coordinate equations.

Choose the best answer. Identify the circle element or theorem, use the appropriate formula, and keep angle measures, radius, diameter, and units consistent.

10 Questions
0/10 Questions0 %
Correct 0
Incorrect 0
Unanswered 10
1. QuestionMultiple choice

Which formula gives the circumference of a circle with radius r?

Please select an answer first.

Correct answer: A

The correct answer is C=2πrC=2\pi r..

  1. Identify the circle information: Mark the center, radius, diameter, chord, arc, angle, tangent, or coordinate information given.
  2. Apply the circle relationship: The circumference formula is C=2πrC=2\pi r, or equivalently C=πdC=\pi d.
  3. Check the result: The correct answer is C=2πrC=2\pi r..

The circumference formula is C=2πrC=2\pi r, or equivalently C=πdC=\pi d.

2. QuestionMultiple choice

Which formula gives the area of a circle with radius r?

Please select an answer first.

Correct answer: B

The correct answer is A=πr2A=\pi r^2..

  1. Identify the circle information: Mark the center, radius, diameter, chord, arc, angle, tangent, or coordinate information given.
  2. Apply the circle relationship: The area of a circle is A=πr2A=\pi r^2.
  3. Check the result: The correct answer is A=πr2A=\pi r^2..

The area of a circle is A=πr2A=\pi r^2.

3. QuestionMultiple choice

What is the circumference of a circle with radius 5?

Please select an answer first.

Correct answer: C

The correct answer is 10π10\pi..

  1. Identify the circle information: Mark the center, radius, diameter, chord, arc, angle, tangent, or coordinate information given.
  2. Apply the circle relationship: Substitute r = 5 into C=2πrC=2\pi r: C=10πC=10\pi.
  3. Check the result: The correct answer is 10π10\pi..

Substitute r = 5 into C=2πrC=2\pi r: C=10πC=10\pi.

4. QuestionMultiple choice

What is the area of a circle with diameter 12?

Please select an answer first.

Correct answer: D

The correct answer is 36π36\pi square units..

  1. Identify the circle information: Mark the center, radius, diameter, chord, arc, angle, tangent, or coordinate information given.
  2. Apply the circle relationship: The radius is 6, so A=π(6)2=36πA=\pi(6)^2=36\pi.
  3. Check the result: The correct answer is 36π36\pi square units..

The radius is 6, so A=π(6)2=36πA=\pi(6)^2=36\pi.

5. QuestionMultiple choice

A circle has circumference 18π18\pi. What is its radius?

Please select an answer first.

Correct answer: A

The correct answer is 9 units..

  1. Identify the circle information: Mark the center, radius, diameter, chord, arc, angle, tangent, or coordinate information given.
  2. Apply the circle relationship: Set 2πr=18π2\pi r=18\pi; dividing by 2π2\pi gives r = 9.
  3. Check the result: The correct answer is 9 units..

Set 2πr=18π2\pi r=18\pi; dividing by 2π2\pi gives r = 9.

6. QuestionMultiple choice

A circle has area 49π49\pi. What is its diameter?

Please select an answer first.

Correct answer: B

The correct answer is 14 units..

  1. Identify the circle information: Mark the center, radius, diameter, chord, arc, angle, tangent, or coordinate information given.
  2. Apply the circle relationship: Since πr2=49π\pi r^2=49\pi, r = 7 and the diameter is 14.
  3. Check the result: The correct answer is 14 units..

Since πr2=49π\pi r^2=49\pi, r = 7 and the diameter is 14.

7. QuestionMultiple choice

What is the circumference of a circle with radius 3?

Please select an answer first.

Correct answer: C

The correct answer is 6π6\pi..

  1. Identify the circle information: Mark the center, radius, diameter, chord, arc, angle, tangent, or coordinate information given.
  2. Apply the circle relationship: Use C=2πr=2π(3)=6πC=2\pi r=2\pi(3)=6\pi.
  3. Check the result: The correct answer is 6π6\pi..

Use C=2πr=2π(3)=6πC=2\pi r=2\pi(3)=6\pi.

8. QuestionMultiple choice

What is the area of a quarter-circle with radius 8?

Please select an answer first.

Correct answer: D

The correct answer is 16π16\pi square units..

  1. Identify the circle information: Mark the center, radius, diameter, chord, arc, angle, tangent, or coordinate information given.
  2. Apply the circle relationship: The full area is 64π64\pi; one quarter is 16π16\pi.
  3. Check the result: The correct answer is 16π16\pi square units..

The full area is 64π64\pi; one quarter is 16π16\pi.

9. QuestionMultiple choice

A circle has circumference 10π10\pi. What is its area?

Please select an answer first.

Correct answer: A

The correct answer is 25π25\pi square units..

  1. Identify the circle information: Mark the center, radius, diameter, chord, arc, angle, tangent, or coordinate information given.
  2. Apply the circle relationship: The circumference gives r = 5, so the area is π(5)2=25π\pi(5)^2=25\pi.
  3. Check the result: The correct answer is 25π25\pi square units..

The circumference gives r = 5, so the area is π(5)2=25π\pi(5)^2=25\pi.

10. QuestionMultiple choice

If one circle has twice the radius of another, how do their areas compare?

Please select an answer first.

Correct answer: B

The correct answer is The larger area is four times the smaller area..

  1. Identify the circle information: Mark the center, radius, diameter, chord, arc, angle, tangent, or coordinate information given.
  2. Apply the circle relationship: Area scales by the square of the radius factor: 22=42^2=4.
  3. Check the result: The correct answer is The larger area is four times the smaller area..

Area scales by the square of the radius factor: 22=42^2=4.

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