Circumference Practice Problems: Calculate Radius & Perimeter

Master circumference calculations with step-by-step practice problems. Learn to find radius from perimeter using the formula P=2πR through guided examples and exercises.

📚What You'll Master in This Circumference Practice Session

Calculate radius from given circumference using the formula P=2πR
Solve real-world problems involving circular paths and running tracks
Find circumference when radius or diameter is provided
Apply circumference formulas to complex geometric shapes with semicircles
Convert between different units in circumference problems
Determine area of circles using circumference information

Understanding How is the radius calculated using its circumference?

Complete explanation with examples

Some of you may know the radius as a "dial". Either way, the meaning is identical with the same characteristics. So, what is the radius? It is a specific segment that connects the center of a circle with a particular point on the circumference .

How is the radius calculated using its perimeter?

The formula for calculating the perimeter or circumference of a circle is: $P=2πR$

Where $P =$ is the perimeter of the circle, $R =$ is the radius of the circle, and $π =$ is a number approximately equal to $3.14$ .

Given: A circle with a circumference of $18.84$ . The radius of the circle needs to be calculated.

We will place the known data into the formula: $18.84=2πR$

The perimeter can be translated in terms of $π$ , that is: $18.84:3.14=6$

Then we obtain: $6π=2πR$

Reduce the value of $π$ and get $6=2R$ . Continue with a division by $2$ to isolate the value of $R$ .

That is: $R=\frac{6}{2}$ and, therefore, the result obtained is that the radius of the circle $=3$ .

1 - How to calculate the radius using its perimeter

Detailed explanation

Practice How is the radius calculated using its circumference?

Test your knowledge with 30 quizzes

$r=\frac{1}{3}$

Calculate the circumference.

Examples with solutions for How is the radius calculated using its circumference?

Step-by-step solutions included

Exercise #1

O is the center of the circle in the diagram.

What is its perimeter?

Step-by-Step Solution

To solve this problem, we will determine the circumference of the circle:

Step 1: Identify the radius, $r$ . From the diagram, the number $4$ is provided, suggesting that $r = 4$ cm.
Step 2: Use the circumference formula for a circle: $C = 2\pi r$ .
Step 3: Substitute the radius into the formula: $C = 2\pi \times 4 = 8\pi$ cm.

Therefore, the circumference of the circle is $8\pi$ cm. This aligns with choice 3 from the provided options.

The correct and verified circumference is $8\pi$ cm.

Answer:

$8\pi$ cm

Video Solution

Exercise #2

$r=7$

Calculate the circumference.

Step-by-Step Solution

To solve the problem of finding the circumference of a circle with radius $r = 7$ , we will follow these steps:

Step 1: Identify the given value of the radius.
Step 2: Apply the formula for the circumference of a circle.
Step 3: Calculate the result using known values.

Let's go through these steps in detail:

Step 1: The radius $r$ is given as $7$ .

Step 2: The formula for the circumference of a circle is $C = 2\pi r$ .

Step 3: Substitute the given radius into the formula:
$C = 2\pi \times 7 = 14\pi$

Using the value of $\pi \approx 3.14159$ , we can calculate:

$C \approx 14 \times 3.14159 \approx 43.982$

Therefore, the circumference of the circle is approximately $43.982$ .

Answer:

43.982

Video Solution

Exercise #3

$r=6$

Calculate the circumference.

Step-by-Step Solution

To solve this problem, follow these steps:

Step 1: Given that the radius $r = 6$ .
Step 2: Use the formula for the circumference of a circle, $C = 2\pi r$ .
Step 3: Substitute the radius into the formula: $C = 2\pi \times 6$ .
Step 4: Calculate the expression: $C = 12\pi$ .
Step 5: Approximate $\pi \approx 3.14159$ to find $C \approx 12 \times 3.14159$ .
Step 6: Perform the multiplication: $C \approx 37.69908$ .
Step 7: Round off the number to three decimal places: $C \approx 37.699$ .

The correct answer matches the choice labeled 2: 37.699.

Answer:

37.699

Video Solution

Exercise #4

$r=11$

Calculate the circumference.

Step-by-Step Solution

To solve this problem, we'll follow these steps:

Step 1: Identify the given information
Step 2: Apply the appropriate formula
Step 3: Perform the necessary calculations

Now, let's work through each step:
Step 1: The problem provides the radius of the circle as $r = 11$ .
Step 2: We'll use the formula for the circumference of a circle: $C = 2\pi r$ .
Step 3: Plugging in the value of the radius, $r = 11$ , into the formula, we get: $C = 2\pi \times 11 = 22\pi$ .
Using approximately $\pi = 3.14159$ , we calculate: $C = 22 \times 3.14159 \approx 69.115$ .

Therefore, the circumference of the circle is approximately 69.115.

Upon comparing this with the given choices, the correct choice is:
Choice 4:

69.115

Answer:

69.115

Video Solution

Exercise #5

Look at the circle in the figure:

Its radius is equal to 4.

What is its circumference?

Step-by-Step Solution

The formula for the circumference is equal to:

$2\pi r$

Answer:

8π

Video Solution

Frequently Asked Questions

Everything you need to know about How is the radius calculated using its circumference?

How do you find the radius from circumference?

To find radius from circumference, use the formula R = P/(2π). Divide the given circumference by 2π (approximately 6.28). For example, if circumference is 18.84, then R = 18.84 ÷ 6.28 = 3.

What is the formula for circumference of a circle?

The circumference formula is P = 2πR, where P is the perimeter, R is the radius, and π ≈ 3.14. You can also use P = πd where d is the diameter.

How do you solve circumference word problems step by step?

Follow these steps: 1) Identify what's given (radius, diameter, or circumference), 2) Choose the correct formula (P = 2πR or R = P/(2π)), 3) Substitute known values, 4) Solve for the unknown variable, 5) Check your answer makes sense.

What's the difference between radius and diameter in circumference problems?

Radius is the distance from center to edge of a circle, while diameter is the full distance across the circle through the center. Diameter = 2 × radius. The circumference formula with diameter is P = πd.

How do you calculate circumference without a calculator?

Use π ≈ 3.14 for easier mental math. For radius 5: P = 2 × 3.14 × 5 = 31.4. You can also use π ≈ 22/7 for fraction calculations. Practice estimation skills by rounding to nearest whole numbers first.

What are common mistakes when solving circumference problems?

Common errors include: confusing radius with diameter, forgetting to multiply by 2 in P = 2πR, using wrong value of π, not converting units properly, and mixing up circumference with area formulas.

How is circumference used in real life applications?

Circumference calculations are used for: designing circular running tracks, calculating wheel rotations and distance traveled, determining material needed for circular borders or fencing, and solving problems involving gears, pulleys, and rotating machinery.

Can you find the area of a circle if you know its circumference?

Yes! First find the radius using R = P/(2π), then calculate area using A = πR². For example, if circumference is 6.28, then R = 1, so A = π × 1² = π square units.

More How is the radius calculated using its circumference? Questions

Click on any question to see the complete solution with step-by-step explanations

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Continue Your Math Journey

Master How is the radius calculated using its circumference? first, then advance to these related topics that build on your fraction skills

Topics Learned in Later Sections

Circle Diameter Pi The Circumference of a Circle The Center of a Circle Radius Perimeter Parts of a Circle Area Elements of the circumference Area of a circle

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