Radius of a Circle: Explanation and Examples

📐 Quick Study Guide: Radius of a Circle

• 🎯 Definition: The radius of a circle is the distance from the exact center of the circle to any point on its boundary (circumference).
• ↔️ Symbol: It is typically represented by the lowercase letter '$r$'.
• 🔗 Relationship to Diameter: The diameter ('$d$') of a circle is twice its radius. This means if you know the radius, $d = 2r$. Conversely, if you know the diameter, $r = \frac{d}{2}$.
• 📏 Constant Length: Every radius in a given circle has the exact same length, no matter which point on the circumference you measure to from the center.
• 🔢 Key in Formulas: The radius is fundamental in calculating a circle's properties:
  • Circumference ($C$): $C = 2\pi r$
  • Area ($A$): $A = \pi r^2$
• 💡 Visualizing: Imagine drawing a line segment from the very middle of a pizza to its crust. That's a radius!
• ✨ Units: The radius is a measure of length, so its units will be meters (m), centimeters (cm), inches (in), etc.

📝 Practice Quiz

Choose the best answer for each question.

1. What is the definition of the radius of a circle?

   1. The distance around the circle.
   2. A line segment connecting two points on the circle's boundary.
   3. The distance from the center of the circle to any point on its boundary.
   4. The longest distance across the circle, passing through the center.

2. If the diameter of a circle is 18 cm, what is its radius?

   1. 36 cm
   2. 9 cm
   3. 18 cm
   4. 6 cm

3. A circle has a radius of 7 meters. What is its diameter?

   1. 7 meters
   2. 14 meters
   3. 3.5 meters
   4. 21 meters

4. Which formula correctly represents the relationship between the diameter ($d$) and the radius ($r$) of a circle?

   1. $d = r^2$
   2. $r = d + 2$
   3. $d = 2r$
   4. $r = d \times 2$

5. The area of a circle is given by the formula $A = \pi r^2$. What does '$r$' represent in this formula?

   1. Circumference
   2. Diameter
   3. Radius
   4. Area

6. If a circle has a radius of 5 units, what would be the length of any other radius drawn in the same circle?

   1. Could be shorter or longer
   2. Exactly 5 units
   3. Cannot be determined without more information
   4. Exactly 10 units

7. A car tire has a radius of 30 cm. If the car travels one full rotation, the distance covered is approximately its circumference. Which value is directly used to calculate this distance using $C=2\pi r$?

   1. 30 cm
   2. 60 cm
   3. 15 cm
   4. 30 cm$^2$