Circles practice questions

Circles questions

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1. 1CirclesFoundation

   A circle has diameter 10. What is its area in terms of π?A circle has diameter 10. What is its area in terms of π?

   • A5π5π
   • B10π10π
   • C25π25π
   • D100π100π
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   Answer: 25π25π

   The radius is half the diameter, so r = 5. Area is π r² = 25π.The radius is half the diameter, so r = 5. Area is π r^2 = 25π.

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2. 2CirclesFoundation

   A circle has a diameter of 18 cm. What is its area, in terms of π?A circle has a diameter of 18 cm. What is its area, in terms of π?

   • A81π square cm81π square cm
   • B324π square cm324π square cm
   • C36π square cm36π square cm
   • D18π square cm18π square cm
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   Answer: 81π square cm81π square cm

   The radius is half the diameter, so 9 cm, and the area is π(9²) = 81π square cm. Using the diameter in place of the radius gives 324π, four times too large.The radius is half the diameter, so 9 cm, and the area is π(9^2) = 81π square cm. Using the diameter in place of the radius gives 324π, four times too large.

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3. 3CirclesFoundation

   A circle has an area of 121π. What is its radius?A circle has an area of 121π. What is its radius?

   • A60.560.5
   • B1111
   • C121121
   • D2222
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   Answer: 1111

   From π r² = 121π comes r² = 121, so r = 11. The choice 121 stops before taking the square root, and 22 is the diameter.From π r^2 = 121π comes r^2 = 121, so r = 11. The choice 121 stops before taking the square root, and 22 is the diameter.

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4. 4CirclesStandard

   A circle has radius 4. What is its circumference in terms of π?A circle has radius 4. What is its circumference in terms of π?

   • A32π32π
   • B4π4π
   • C16π16π
   • D8π8π
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   Answer: 8π8π

   Circumference is 2π r. With r = 4, the circumference is 8π.Circumference is 2π r. With r = 4, the circumference is 8π.

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5. 5CirclesStandard

   A circle has center (2, -3) and radius 5. Which equation describes it?A circle has center (2, -3) and radius 5. Which equation describes it?

   • A(x - 2)² + (y + 3)² = 25(x - 2)^2 + (y + 3)^2 = 25
   • B(x - 2)² + (y + 3)² = 5(x - 2)^2 + (y + 3)^2 = 5
   • C(x + 2)² + (y - 3)² = 25(x + 2)^2 + (y - 3)^2 = 25
   • D(x - 2)² + (y - 3)² = 25(x - 2)^2 + (y - 3)^2 = 25
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   Answer: (x - 2)² + (y + 3)² = 25(x - 2)^2 + (y + 3)^2 = 25

   The equation is (x - h)² + (y - k)² = r². With center (2, -3), y - (-3) becomes y + 3, and the right side is 5² = 25.The equation is (x - h)^2 + (y - k)^2 = r^2. With center (2, -3), y - (-3) becomes y + 3, and the right side is 5^2 = 25.

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6. 6CirclesStandard

   A sector of a circle of radius 6 has a central angle of 60°. What is its area in terms of π?A sector of a circle of radius 6 has a central angle of 60°. What is its area in terms of π?

   • A3π3π
   • B12π12π
   • C6π6π
   • D36π36π
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   Answer: 6π6π

   A 60-degree sector is one sixth of the circle. The full area is 36π, so the sector is 36π / 6 = 6π.A 60-degree sector is one sixth of the circle. The full area is 36π, so the sector is 36π / 6 = 6π.

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7. 7CirclesStandard

   A circle has a circumference of 36π. Enter its radius.A circle has a circumference of 36π. Enter its radius.

   Student-produced response: write your own answer rather than choosing one.

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   Answer: 1818

   Circumference is 2π r, so 2π r = 36π gives r = 18. Using the area formula instead is the usual wrong turn here.Circumference is 2π r, so 2π r = 36π gives r = 18. Using the area formula instead is the usual wrong turn here.

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8. 8CirclesStandard

   A circle has an area of 49π. What is its circumference, in terms of π?A circle has an area of 49π. What is its circumference, in terms of π?

   • A7π7π
   • B14π14π
   • C49π49π
   • D98π98π
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   Answer: 14π14π

   From π r² = 49π comes r² = 49, so r = 7. The circumference is 2π r = 14π. Answering 7π uses the radius where the diameter belongs.From π r^2 = 49π comes r^2 = 49, so r = 7. The circumference is 2π r = 14π. Answering 7π uses the radius where the diameter belongs.

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9. 9CirclesStandard

   A circle has a circumference of 44π. What is its radius?A circle has a circumference of 44π. What is its radius?

   • A4444
   • B1111
   • C2222
   • D8888
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   Answer: 2222

   Circumference is 2π r, so 2r = 44 and r = 22. Halving twice gives 11, which is the radius of a circle with half this circumference.Circumference is 2π r, so 2r = 44 and r = 22. Halving twice gives 11, which is the radius of a circle with half this circumference.

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10. 10CirclesChallenge

    If a circle's radius is doubled, by what factor does its area increase?If a circle's radius is doubled, by what factor does its area increase?

    • A44
    • B88
    • C1616
    • D22
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    Answer: 44

    Area is π r². Replacing r with 2r gives π(2r)² = 4π r², so the area is 4 times as large.Area is π r^2. Replacing r with 2r gives π(2r)^2 = 4π r^2, so the area is 4 times as large.

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11. 11CirclesChallenge

    A circle has area 36π. Enter its circumference divided by π.A circle has area 36π. Enter its circumference divided by π.

    Student-produced response: write your own answer rather than choosing one.

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    Answer: 1212

    From π r² = 36π, r² = 36 and r = 6. The circumference is 2π r = 12π, so dividing by π gives 12.From π r^2 = 36π, r^2 = 36 and r = 6. The circumference is 2π r = 12π, so dividing by π gives 12.

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12. 12CirclesChallenge

    A circle has equation (x - 3)² + (y + 1)² = 49. What is its radius?A circle has equation (x - 3)^2 + (y + 1)^2 = 49. What is its radius?

    • A24.524.5
    • B1414
    • C4949
    • D77
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    Answer: 77

    The standard form sets the right-hand side to r², so r² = 49 and r = 7. Reading 49 as the radius skips the square root.The standard form sets the right-hand side to r^2, so r^2 = 49 and r = 7. Reading 49 as the radius skips the square root.

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13. 13CirclesChallenge

    A circle has its center at (3, -2) and passes through the point (7, 1). What is its radius?A circle has its center at (3, -2) and passes through the point (7, 1). What is its radius?

    • A2525
    • Bthe square root of 7the square root of 7
    • C55
    • D77
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    Answer: 55

    The radius is the distance from the center to the point: the gaps are 4 and 3, so the radius is the square root of 16 + 9 = 25, which is 5. The choice 25 stops one step early, at the square of the radius.The radius is the distance from the center to the point: the gaps are 4 and 3, so the radius is the square root of 16 + 9 = 25, which is 5. The choice 25 stops one step early, at the square of the radius.

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14. 14CirclesChallenge

    A sector of a circle of radius 12 has a central angle of 60°. What is the area of the sector, in terms of π?A sector of a circle of radius 12 has a central angle of 60°. What is the area of the sector, in terms of π?

    • A12π12π
    • B24π24π
    • C48π48π
    • D144π144π
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    Answer: 24π24π

    A 60-degree sector is 60360 = one sixth of the circle. The whole circle has area π(12²) = 144π, so the sector has 144π / 6 = 24π. The choice 144π is the whole circle.A 60-degree sector is 60/360 = one sixth of the circle. The whole circle has area π(12^2) = 144π, so the sector has 144π / 6 = 24π. The choice 144π is the whole circle.

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15. 15CirclesChallenge

    A sector of a circle of radius 8 has a central angle of 90°. What is its area, in terms of π?A sector of a circle of radius 8 has a central angle of 90°. What is its area, in terms of π?

    • A64π64π
    • B32π32π
    • C8π8π
    • D16π16π
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    Answer: 16π16π

    A 90-degree sector is a quarter of the circle. The whole circle has area 64π, so the sector has 16π. The choice 64π is the whole circle and 32π is half of it.A 90-degree sector is a quarter of the circle. The whole circle has area 64π, so the sector has 16π. The choice 64π is the whole circle and 32π is half of it.

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16. 16CirclesChallenge

    A sector of a circle of radius 9 has a central angle of 120°. Enter the area of the sector as a multiple of π.A sector of a circle of radius 9 has a central angle of 120°. Enter the area of the sector as a multiple of π.

    Student-produced response: write your own answer rather than choosing one.

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    Answer: 2727

    A 120-degree sector is one third of the circle. The whole circle has area 81π, so the sector has 27π.A 120-degree sector is one third of the circle. The whole circle has area 81π, so the sector has 27π.

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