Quiz on Circumference and Arc Length for Sophomores

📐 Quick Study Guide

• 🧮 Circumference of a Circle: The distance around the circle is calculated using the formula $C = 2\pi r$, where $r$ is the radius.
• 🔴 Radius and Diameter: The radius ($r$) is half the diameter ($d$), so $r = \frac{d}{2}$. Therefore, $C = \pi d$.
• 弧 Arc Length: The length of an arc is a fraction of the circle's circumference. The formula is: Arc Length $= \frac{\theta}{360} \cdot 2\pi r$, where $\theta$ is the central angle in degrees.
• 扇 Sector Area (Related Concept): The area of a sector is $A = \frac{\theta}{360} \cdot \pi r^2$, useful for some problems.
• 💡 Key Tip: Always make sure your units are consistent (e.g., if the radius is in cm, the circumference will be in cm too).
• ✍️ Remember $\pi$: $\pi$ is approximately 3.14159. Use the $\pi$ button on your calculator for more accuracy!

🧪 Practice Quiz

1. What is the circumference of a circle with a radius of 7 cm?
   1. 14$\pi$ cm
   2. 7$\pi$ cm
   3. 49$\pi$ cm
   4. 21$\pi$ cm
2. A circle has a diameter of 10 inches. What is its circumference?
   1. 5$\pi$ inches
   2. 10$\pi$ inches
   3. 20$\pi$ inches
   4. 100$\pi$ inches
3. An arc has a central angle of 90 degrees in a circle with a radius of 4 inches. What is the arc length?
   1. $\pi$ inches
   2. 2$\pi$ inches
   3. 4$\pi$ inches
   4. 8$\pi$ inches
4. If the circumference of a circle is 24$\pi$ meters, what is the radius?
   1. 6 meters
   2. 12 meters
   3. 24 meters
   4. 48 meters
5. An arc length is 5$\pi$ cm and the radius of the circle is 10 cm. What is the central angle of the arc?
   1. 45 degrees
   2. 60 degrees
   3. 90 degrees
   4. 180 degrees
6. What is the diameter of a circle with a circumference of 18$\pi$ cm?
   1. 6 cm
   2. 9 cm
   3. 18 cm
   4. 36 cm
7. An arc with a central angle of 60 degrees has a length of 3$\pi$ meters. What is the radius of the circle?
   1. 6 meters
   2. 9 meters
   3. 12 meters
   4. 18 meters