Circumference: Applying the formula

Formula of the circumference:

$P=2\pi r$

We insert the given data into the formula:

$P=2\times6\times\pi$

$P=12\pi$

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

• Step 1: Identify the formula for the circumference of a circle as $C = 2\pi r$.
• Step 2: Substitute the known value of the radius into the formula.
• Step 3: Simplify to find the circumference.

Now, let's work through each step:
Step 1: The formula for the circumference, $C$, is $C = 2\pi r$.
Step 2: Substitute the given radius $r = 3$ cm into the formula:
$C = 2\pi \times 3$.
Step 3: Perform the multiplication:
$C = 6\pi$.
Thus, the circumference of the circle is $6\pi$ cm.

Therefore, the solution to the problem is $6\pi$ cm.

The formula for the circumference is equal to:

$2\pi r$

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 gives us the radius of the circle, $r = 2$.
Step 2: We'll use the formula for the circumference of a circle, which is $C = 2\pi r$.
Step 3: Substituting the radius into the formula, we get $C = 2 \times \pi \times 2 = 4\pi$.
Assuming $\pi$ is approximately 3.14, we calculate $C = 4 \times 3.14 = 12.56$.

Therefore, the circumference of the circle is $12.56$.

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.

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 $43.982$.

We use the formula:$P=2\pi r$

We replace the data in the formula:$P=2\times8\pi$

$P=16\pi$

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

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.

To solve this problem, we'll calculate the circumference of a circle using the formula $C = 2\pi r$.

• Step 1: Identify the given radius $r = \frac{1}{3}$.
• Step 2: Use the formula for circumference $C = 2\pi r$.
• Step 3: Substitute the radius into the formula: $C = 2\pi \times \frac{1}{3}$.
• Step 4: Simplify the expression to get $C = \frac{2\pi}{3}$.
• Step 5: Use an approximate value for $\pi \approx 3.14159$ to compute: $C \approx \frac{2 \times 3.14159}{3}$.
• Step 6: Calculate to obtain $C \approx 2.094$.

Therefore, the circumference of the circle is approximately $2.094$.

This matches choice 4 in the given multiple-choice answers.

To solve this problem, we will follow these steps:

• Step 1: Identify the given information - the radius $r = 29$.
• Step 2: Apply the formula for the circumference of a circle, which is $C = 2\pi r$.
• Step 3: Perform the calculations using $\pi \approx 3.14159$.

Now, let's work through each step:

Step 1: We are given the radius $r = 29$.

Step 2: The formula for the circumference is $C = 2\pi r$. Substituting the value of $r$, we get:

$C = 2 \times \pi \times 29$.

Step 3: Calculate the expression:

$C = 2 \times 3.14159 \times 29$.

$C \approx 182.212$.

Therefore, the circumference of the circle is approximately $182.212$.

Hence, the solution to the problem is 182.212.

To solve this problem, we'll use the formula for the circumference of a circle, which is:

$C = 2\pi r$

Given that the radius $r$ is 8.5, we substitute this value into the formula:

$C = 2 \pi \times 8.5$

Using the approximation $\pi \approx 3.14159$, the formula becomes:

$C = 2 \times 3.14159 \times 8.5$

Calculate the multiplication:

$C = 53.40707$

After rounding to three decimal places, the circumference is $C = 53.407$.

The circumference of the circle is therefore $53.407$.

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: We are given the radius of the circle $r = 8.7$.

Step 2: We'll use the formula for the circumference of a circle: $C = 2 \pi r$.

Step 3: Plugging in our value for the radius, we calculate:
$C = 2 \pi (8.7)$

Using $\pi \approx 3.14159$, the expression becomes:
$C = 2 \times 3.14159 \times 8.7$

Performing the multiplication, we get:
$C \approx 54.664$

Therefore, the circumference of the circle is approximately $54.664$.

This matches the answer choice : 54.664

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

To solve this problem, we'll go through the following steps:

• Calculate the circumference of the circular park.
• Determine the total distance Ivan runs.
• Find Ivan's average speed.

Step 1: Calculate the circumference of the circular park.
The formula for the circumference of a circle is $C = 2\pi r$, where $r$ is the radius.
Given $r = 300$ meters, $C = 2\pi \times 300 = 600\pi$ meters.

Step 2: Determine the total distance Ivan runs.
Ivan completes 5 laps, so the total distance $D$ is given by:
$D = 5 \times 600\pi = 3000\pi$ meters.

Step 3: Find Ivan's average speed.
The formula for average speed is $v = \frac{\text{total distance}}{\text{total time}}$.
Total time = 35 minutes.
Average speed $v = \frac{3000\pi}{35} \approx 269.14$ meters per minute.

Therefore, Ivan's average speed is $269.14$ meters per minute.