Circles — Practice Quiz

A Geometry cheat sheet for Circles — every key formula with its symbols defined — plus a medium-level practice quiz to test recall.

Formulas & key concepts

Circumference

$$C = 2\pi r = \pi d$$

Where: \(r\) = radius, \(d\) = diameter

Area of Circle

$$A = \pi r^2$$

Sector Area

$$A_{sector} = \frac{1}{2}r^2\theta$$

Where: \(\theta\) = angle in radians

Arc Length

$$L_{arc} = r\theta$$

Where: \(\theta\) = angle in radians

Circular Segment Area

$$A_{segment} = \frac{1}{2}r^2(\theta - \sin\theta)$$

Practice quiz

  1. A circle has a radius of $7 \text{ cm}$. What is its circumference?

    • $14 \pi \text{ cm}$
    • $7 \pi \text{ cm}$
    • $49 \pi \text{ cm}$
    • $28 \pi \text{ cm}$

    Answer: $14 \pi \text{ cm}$

  2. Calculate the area of a circle with a diameter of $10 \text{ m}$.

    • $100 \pi \text{ m}^2$
    • $25 \pi \text{ m}^2$
    • $10 \pi \text{ m}^2$
    • $50 \pi \text{ m}^2$

    Answer: $25 \pi \text{ m}^2$

  3. A circle has a radius of $6 \text{ cm}$. What is the length of an arc subtended by a central angle of $\frac{\pi}{3}$ radians?

    • $6 \pi \text{ cm}$
    • $2 \pi \text{ cm}$
    • $12 \pi \text{ cm}$
    • $3 \pi \text{ cm}$

    Answer: $2 \pi \text{ cm}$

  4. Find the area of a circular sector with a radius of $4 \text{ m}$ and a central angle of $\frac{\pi}{2}$ radians.

    • $16 \pi \text{ m}^2$
    • $8 \pi \text{ m}^2$
    • $4 \pi \text{ m}^2$
    • $2 \pi \text{ m}^2$

    Answer: $4 \pi \text{ m}^2$

  5. If the circumference of a circle is $18 \pi \text{ cm}$, what is its radius?

    • $9 \text{ cm}$
    • $18 \text{ cm}$
    • $3 \text{ cm}$
    • $6 \text{ cm}$

    Answer: $9 \text{ cm}$

  6. An arc of a circle has a length of $5 \pi \text{ cm}$ and the circle has a radius of $10 \text{ cm}$. What is the central angle in radians?

    • $\pi \text{ rad}$
    • $\frac{\pi}{2} \text{ rad}$
    • $2\pi \text{ rad}$
    • $\frac{\pi}{4} \text{ rad}$

    Answer: $\frac{\pi}{2} \text{ rad}$

  7. A circular sector has an area of $12 \pi \text{ m}^2$ and a radius of $6 \text{ m}$. What is the central angle in radians?

    • $\frac{\pi}{3} \text{ rad}$
    • $\frac{2\pi}{3} \text{ rad}$
    • $\pi \text{ rad}$
    • $\frac{4\pi}{3} \text{ rad}$

    Answer: $\frac{2\pi}{3} \text{ rad}$

  8. A circular segment is formed in a circle with a radius of $2 \text{ m}$ by a central angle of $\frac{\pi}{2}$ radians. Calculate the area of the segment.

    • $(\pi - 1) \text{ m}^2$
    • $(\pi - 2) \text{ m}^2$
    • $(2\pi - 2) \text{ m}^2$
    • $(\frac{\pi}{2} - 1) \text{ m}^2$

    Answer: $(\pi - 2) \text{ m}^2$

  9. A circular garden has a circumference of $20 \pi \text{ m}$. What is the area of the garden?

    • $400 \pi \text{ m}^2$
    • $100 \pi \text{ m}^2$
    • $20 \pi \text{ m}^2$
    • $40 \pi \text{ m}^2$

    Answer: $100 \pi \text{ m}^2$

  10. A sector of a circle has an arc length of $3\pi \text{ cm}$ and a radius of $9 \text{ cm}$. What is the area of this sector?

    • $\frac{9\pi}{2} \text{ cm}^2$
    • $\frac{27\pi}{2} \text{ cm}^2$
    • $9\pi \text{ cm}^2$
    • $27\pi \text{ cm}^2$

    Answer: $\frac{27\pi}{2} \text{ cm}^2$

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