Calculate Circle Perimeter: Given Radius = 2/3 Units

Q: What's the difference between perimeter and circumference?

For circles, perimeter and circumference mean the exact same thing - the distance around the outside edge. We usually say 'circumference' for circles and 'perimeter' for other shapes.

Q: How do I multiply 2 times 2/3?

Think of 2 as $ \frac{2}{1} $, then multiply: $ \frac{2}{1} \times \frac{2}{3} = \frac{4}{3} $. Multiply the tops together and bottoms together!

Q: Why don't I multiply π by anything?

π is just a constant number (approximately 3.14). We leave it as π in our final answer $ \frac{4}{3}\pi $ because that's the exact answer!

Q: Should I convert 2/3 to a decimal first?

No! Keep fractions as fractions throughout your work. Converting to decimals early can introduce rounding errors and make your final answer less accurate.

Q: How do I know which formula to use?

Given radius: Use C = 2πrGiven diameter: Use C = πdRemember: diameter = 2 × radius

Q: Can I simplify 4/3π any further?

No, $ \frac{4}{3}\pi $ is already in simplest form! The fraction 4/3 cannot be reduced, and we keep π as a symbol for the exact answer.

Circle Circumference with Fractional Radius

Look at the circle in the figure.

The radius of the circle is $\frac{2}{3}$ .

What is its perimeter?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the circumference of the circle

00:03 We will use the formula for calculating circle circumference

00:14 We will substitute the radius value according to the given data and solve for the circumference

00:29 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Look at the circle in the figure.

The radius of the circle is $\frac{2}{3}$ .

What is its perimeter?

Step-by-step solution

The radius is a straight line that extends from the center of the circle to its outer edge.

The radius is essential for calculating the circumference of the circle, which can be found using the following formula:

If we substitute in the radius we have, the formula will be:

2*π*2/3

To solve this, first we'll rearrange the formula like so:

π*2*2/3 =

We'll then multiply the fraction by the whole number:

π*(2*2)/3 =

π*4/3 =

4/3π

Final Answer

$\frac{4}{3}\pi$

Key Points to Remember

Essential concepts to master this topic

Formula: Circumference equals 2 times pi times radius
Technique: Substitute $\frac{2}{3}$ into $2\pi r = 2\pi \cdot \frac{2}{3}$
Check: Multiply fractions first: $2 \cdot \frac{2}{3} = \frac{4}{3}$ then add π ✓

Common Mistakes

Avoid these frequent errors

Using diameter formula instead of radius formula
Don't use πd when given radius = wrong formula gives wrong answer! The diameter formula πd only works when you know the diameter. Always use C = 2πr when given the radius.

Practice Quiz

Test your knowledge with interactive questions

$$ r=2 $$

Calculate the circumference.

FAQ

Everything you need to know about this question

What's the difference between perimeter and circumference?

For circles, perimeter and circumference mean the exact same thing - the distance around the outside edge. We usually say 'circumference' for circles and 'perimeter' for other shapes.

How do I multiply 2 times 2/3?

Think of 2 as $\frac{2}{1}$ , then multiply: $\frac{2}{1} \times \frac{2}{3} = \frac{4}{3}$ . Multiply the tops together and bottoms together!

Why don't I multiply π by anything?

π is just a constant number (approximately 3.14). We leave it as π in our final answer $\frac{4}{3}\pi$ because that's the exact answer!

Should I convert 2/3 to a decimal first?

No! Keep fractions as fractions throughout your work. Converting to decimals early can introduce rounding errors and make your final answer less accurate.

How do I know which formula to use?

Given radius: Use C = 2πr
Given diameter: Use C = πd
Remember: diameter = 2 × radius

Can I simplify 4/3π any further?

No, $\frac{4}{3}\pi$ is already in simplest form! The fraction 4/3 cannot be reduced, and we keep π as a symbol for the exact answer.

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