Circles

Description: Circles Quiz: Test your understanding of the properties and characteristics of circles.
Number of Questions: 14
Created by:
Tags: geometry circles area circumference radius diameter
Attempted 0/14 Correct 0 Score 0

What is the formula for the circumference of a circle?

  1. C = πd

  2. C = 2πr

  3. C = πr^2

  4. C = 2πd


Correct Option: B
Explanation:

The circumference of a circle is the distance around the circle. It is calculated by multiplying the diameter of the circle by π.

What is the formula for the area of a circle?

  1. A = πr^2

  2. A = 2πr

  3. A = πd

  4. A = 2πd^2


Correct Option: A
Explanation:

The area of a circle is the amount of space inside the circle. It is calculated by multiplying the square of the radius of the circle by π.

What is the relationship between the radius and diameter of a circle?

  1. Radius = 2 * Diameter

  2. Diameter = 2 * Radius

  3. Radius = Diameter

  4. Diameter = Radius


Correct Option: B
Explanation:

The diameter of a circle is the distance across the circle through the center. It is twice the length of the radius.

What is the equation of a circle with center (h, k) and radius r?

  1. (x - h)^2 + (y - k)^2 = r^2

  2. (x + h)^2 + (y + k)^2 = r^2

  3. (x - h)^2 - (y - k)^2 = r^2

  4. (x + h)^2 - (y + k)^2 = r^2


Correct Option: A
Explanation:

The equation of a circle with center (h, k) and radius r is given by (x - h)^2 + (y - k)^2 = r^2.

If the radius of a circle is doubled, what happens to the circumference?

  1. It is doubled

  2. It is quadrupled

  3. It is halved

  4. It remains the same


Correct Option: A
Explanation:

If the radius of a circle is doubled, the circumference is also doubled.

If the radius of a circle is tripled, what happens to the area?

  1. It is tripled

  2. It is quadrupled

  3. It is halved

  4. It remains the same


Correct Option: B
Explanation:

If the radius of a circle is tripled, the area is quadrupled.

What is the diameter of a circle with circumference 20π?

  1. 10

  2. 20

  3. 30

  4. 40


Correct Option: A
Explanation:

The circumference of a circle is given by C = 2πr, where r is the radius. If the circumference is 20π, then the radius is 10.

What is the area of a circle with radius 7 cm?

  1. 49π cm^2

  2. 147π cm^2

  3. 196π cm^2

  4. 225π cm^2


Correct Option: B
Explanation:

The area of a circle is given by A = πr^2, where r is the radius. If the radius is 7 cm, then the area is 147π cm^2.

A circle has a diameter of 12 cm. What is the length of its radius?

  1. 3 cm

  2. 4 cm

  3. 6 cm

  4. 8 cm


Correct Option: C
Explanation:

The diameter of a circle is twice the length of its radius. If the diameter is 12 cm, then the radius is 6 cm.

What is the equation of the circle that passes through the points (2, 3), (4, 5), and (6, 7)?

  1. (x - 4)^2 + (y - 5)^2 = 4

  2. (x - 4)^2 + (y - 5)^2 = 8

  3. (x - 4)^2 + (y - 5)^2 = 12

  4. (x - 4)^2 + (y - 5)^2 = 16


Correct Option: B
Explanation:

The equation of a circle that passes through three non-collinear points can be found using the following formula: ((x - h)^2 + (y - k)^2 = r^2), where (h, k) is the center of the circle and r is the radius. Using the three given points, we can find the center and radius of the circle and then write the equation of the circle.

A circle has an area of 36π square units. What is the length of its radius?

  1. 3 units

  2. 4 units

  3. 5 units

  4. 6 units


Correct Option: D
Explanation:

The area of a circle is given by (A = πr^2), where r is the radius. If the area is 36π square units, then the radius is 6 units.

What is the circumference of a circle with a diameter of 14 cm?

  1. 14π cm

  2. 22π cm

  3. 28π cm

  4. 44π cm


Correct Option: B
Explanation:

The circumference of a circle is given by (C = πd), where d is the diameter. If the diameter is 14 cm, then the circumference is 22π cm.

A circle has a radius of 10 cm. What is the length of a chord that is 8 cm away from the center of the circle?

  1. 6 cm

  2. 8 cm

  3. 10 cm

  4. 12 cm


Correct Option: B
Explanation:

The length of a chord that is d units away from the center of a circle with radius r is given by (\sqrt{r^2 - d^2}). If the radius is 10 cm and the chord is 8 cm away from the center, then the length of the chord is 8 cm.

What is the area of the sector of a circle with radius 12 cm and central angle 60 degrees?

  1. 18π cm^2

  2. 36π cm^2

  3. 54π cm^2

  4. 72π cm^2


Correct Option: B
Explanation:

The area of a sector of a circle is given by (A = \frac{θ}{360}πr^2), where θ is the central angle in degrees, r is the radius, and π is the constant pi. If the radius is 12 cm and the central angle is 60 degrees, then the area of the sector is 36π cm^2.

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