Understanding Circles

Hello, Year 4! Today, we’re going to learn about circles and semi-circles. Let’s dive into some fun facts!

What is a Circle?

A circle is a round shape where every point on the edge is the same distance from the centre. This distance is called the radius.

  • Centre: The middle point of the circle.
  • Radius: The distance from the centre to any point on the edge.
  • Diameter: The distance across the circle, passing through the centre. The diameter is twice the radius. So, if the radius is $$r$$, then the diameter $$d = 2r$$.

Key Rules:

  1. The radius is half of the diameter.
  2. The diameter is double the radius.
  3. A circle has no corners or edges; it’s smooth and round.

Example:

If a circle has a radius of 4 cm, what is its diameter?

Answer: The diameter would be $$d = 2 \times 4 = 8$$ cm.

What is a Semi-Circle?

A semi-circle is half of a circle. Imagine cutting a circle down the middle!

Key Points:

  • A semi-circle still has a radius and a diameter.
  • The curved edge is half of the circle’s edge.
  • The straight edge is the diameter of the full circle.

Example:

If a circle has a radius of 5 cm, the radius of the semi-circle is still 5 cm, and the diameter is $$d = 2 \times 5 = 10$$ cm.

Tips and Tricks for Remembering

  • To find the diameter, remember: double the radius.
  • To find the radius, remember: half the diameter.
  • When working with semi-circles, know that they still use the same rules as circles!

Questions

Easy Level Questions

  1. What is the radius of a circle with a diameter of 10 cm?
  2. If the radius of a circle is 3 cm, what is the diameter?
  3. How many degrees are in a full circle?
  4. Draw a circle and label the centre and radius.
  5. What shape do you get when you cut a circle in half?
  6. If a circle has a radius of 6 cm, what is the diameter?
  7. What do we call the middle point of a circle?
  8. How many radii make up a diameter?
  9. If a semi-circle has a radius of 4 cm, what is its diameter?
  10. Can a circle have corners? Why or why not?

Medium Level Questions

  1. A circle’s radius is 7 cm. What is the diameter?
  2. If a circle’s diameter is 12 cm, what is the radius?
  3. How would you draw a semi-circle?
  4. What is the circumference of a circle with a radius of 5 cm? (Hint: Use $$C = 2 \pi r$$)
  5. If a circle has a radius of 8 cm, what is the area? (Hint: Use $$A = \pi r^2$$)
  6. What is the radius of a circle if its diameter is 14 cm?
  7. Can a semi-circle have a radius and a diameter? Explain.
  8. If you know the diameter is 20 cm, calculate the radius.
  9. How many semi-circles fit into a full circle?
  10. Draw a semi-circle with a radius of 5 cm.

Hard Level Questions

  1. Calculate the diameter of a circle with a circumference of 31.4 cm. (Hint: Use $$C = \pi d$$)
  2. If a circle has an area of 50.24 cm², what is the radius? (Use $$A = \pi r^2$$)
  3. A circle has a radius of 10 cm. Calculate its diameter and circumference.
  4. If a semi-circle has a diameter of 16 cm, what is its area? (Hint: Use $$A = \frac{1}{2} \pi r^2$$)
  5. Calculate the radius of a circle with a circumference of 62.83 cm.
  6. How would you find the area of a circle if you only know the diameter?
  7. If a semi-circle has a radius of 7 cm, what is the length of the curved part?
  8. Create a real-life example where you might see a circle or semi-circle.
  9. If you draw a circle and a semi-circle with the same radius, which one has a larger area? Explain why.
  10. How would you calculate the diameter if you only know the area of a circle?

Answers

Easy Level Answers

  1. 5 cm
  2. 6 cm
  3. 360 degrees
  4. (Student’s drawing)
  5. A semi-circle
  6. 12 cm
  7. Centre
  8. 2
  9. 8 cm
  10. No, because circles have no corners.

Medium Level Answers

  1. 14 cm
  2. 6 cm
  3. Draw a line from the centre to the edge, then draw the edge.
  4. 31.4 cm
  5. 200.96 cm²
  6. 7 cm
  7. Yes, both have a radius and diameter.
  8. 10 cm
  9. One circle can fit into one semi-circle.
  10. (Student’s drawing)

Hard Level Answers

  1. 10 cm
  2. 4 cm
  3. Diameter: 20 cm, Circumference: 62.83 cm
  4. 88 cm²
  5. 10 cm
  6. Divide the diameter by 2 to get the radius, then use the area formula.
  7. 43.98 cm
  8. (Student’s example)
  9. The circle has a larger area because it is a full shape.
  10. Use the area formula to find the radius, then double it for the diameter.

I hope this helps you understand circles and semi-circles better! Keep practicing, and soon you will be a pro at it!