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What is the Property: Diameter = 2 × Radius?
Grade Level:
Class 4
Geometry, Computing, AI, Physics
Definition
What is it?
The property 'Diameter = 2 × Radius' tells us that the diameter of any circle is always twice as long as its radius. The radius is the distance from the center of the circle to any point on its edge, while the diameter is the distance across the circle passing through its center.
Simple Example
Quick Example
Imagine you have a round roti. If you measure from the center of the roti to its edge, that's the radius. If you measure straight across the roti, passing through its center, that's the diameter. The diameter will always be exactly double the length of the radius.
Worked Example
Step-by-Step
PROBLEM: A circular swimming pool has a radius of 5 meters. What is its diameter?
---STEP 1: Understand the relationship. We know that Diameter = 2 × Radius.
---STEP 2: Identify the given value. The radius is 5 meters.
---STEP 3: Substitute the value into the formula. Diameter = 2 × 5 meters.
---STEP 4: Perform the multiplication. Diameter = 10 meters.
---ANSWER: The diameter of the swimming pool is 10 meters.
Why It Matters
Understanding this property is fundamental in geometry, helping engineers design round objects like wheels and pipes accurately. It's crucial in physics for calculating circular motion and even in computing for graphics. Architects and city planners use it to design roundabouts and domes.
Common Mistakes
MISTAKE: Thinking diameter is half the radius. | CORRECTION: Diameter is always double the radius. Remember, the diameter goes all the way across the circle.
MISTAKE: Measuring diameter without passing through the center. | CORRECTION: For a measurement to be the true diameter, it MUST pass through the exact center of the circle. Any other line across is a chord, not the diameter.
MISTAKE: Confusing radius and diameter in calculations. | CORRECTION: Always double-check if the problem gives you the radius or the diameter before applying formulas. If you have the diameter and need the radius, you divide by 2.
Practice Questions
Try It Yourself
QUESTION: A bicycle wheel has a radius of 30 cm. What is its diameter? | ANSWER: 60 cm
QUESTION: A round table has a diameter of 140 cm. What is its radius? | ANSWER: 70 cm
QUESTION: A circular rangoli design has a radius of 45 cm. If you want to draw a line straight across its center, what would be the length of that line? | ANSWER: 90 cm
MCQ
Quick Quiz
If the radius of a bangle is 3 cm, what is its diameter?
1.5 cm
3 cm
6 cm
9 cm
The Correct Answer Is:
C
The diameter is twice the radius. So, 2 multiplied by 3 cm gives 6 cm. Options A, B, and D are incorrect because they do not follow this rule.
Real World Connection
In the Real World
This property is used daily! When you buy a pizza, its size is often given by its diameter (e.g., a 12-inch pizza). When engineers at ISRO design parts for rockets, they use this relationship to ensure circular components like fuel tanks fit perfectly. Even a local carpenter making a round table uses this concept to cut the wood correctly.
Key Vocabulary
Key Terms
RADIUS: Distance from the center of a circle to its edge | DIAMETER: Distance across a circle passing through its center | CIRCLE: A round shape where all points on the edge are the same distance from the center | CENTER: The middle point of a circle
What's Next
What to Learn Next
Now that you understand diameter and radius, you can move on to learning about the circumference of a circle. The circumference is the distance around the circle, and it uses both the diameter and a special number called pi (π).
