How to calculate the Circumference of a circle exactly?

The circumference of a circle is a basic and required math knowledge introduced in elementary or middle school. Mastering the circumference of a circle is essential for students who plan to pursue more advanced mathematics courses in high school and college and prepare for standardized exams such as the SAT and ACT.

The 10 Circumference of a Circle Quiz in this article is designed to test your understanding of finding the radius, diameter, and circumference of a circle.

**Table of Contents:**

- Circumference of a circle formula
- Circumference of a circle quiz
- Key takeaways
- Frequently Asked Questions

## Circumference of a circle formula

Before taking a test, let's recap some crucial information!

**What is the circumference of a circle?**

The circumference of a circle is the linear distance of a circle's edge. It is equivalent to the perimeter of a geometric shape, although the term perimeter is only used for polygons.

**How to find the circumference of a circle?**

The circumference of a circle formula is:

```
C = 2πr
```

where:

- C is the circumference
- π (pi) is a mathematical constant approximately equal to 3.14159
- r is the radius of the circle

The radius is the distance from the center of the circle to any point on the edge.

The diameter is twice the radius, so the circumference can also be expressed as:

```
C = πd
```

where:

- d is the diameter

For example, if the radius of a circle is 5 cm, then the circumference is:

```
C = 2πr = 2π * 5 cm = 10π cm
```

≈ 31.4 cm (rounded to 2 decimal places)

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## Circumference of a circle quiz

**Question 1: If the circumference of a circular swimming pool is 50 meters, what is its radius?**

A. 7.95 meters

B. 8.00 meters

C. 15.91 meters

D. 25 meters

✅ **Correct Answer:**

A. 7.95 meters

**Explanation:**

The radius can be found by rearranging the formula C = 2πr and solving for r: r = C / (2π). Plugging in the given circumference of 50 meters and approximating π to 3.14, we find the radius to be approximately 7.95 meters.

**Question 2: The diameter of a circle is 14 inches. What is its radius?**

A. 28 inches

B.14 inches

C. 21 inches

D. 7 inches

✅ **Correct Answer:**

D. 7 inches

**Explanation:**

Since the diameter is twice the length of the radius (d = 2r), you can find the radius by dividing the diameter by 2 (r = d / 2).In this case, dividing the given diameter of 14 inches by 2 yields a radius of 7 inches.

**Question 3: Which of the following statements is true about the relationship between the diameter and the circumference of a circle?**

A. The diameter is half the circumference.

B. The diameter is the same as the circumference.

C. The diameter is twice the circumference.

D. The diameter is π times the circumference.

✅ **Correct Answer:**

A. The diameter is half the circumference.

**Explanation:**

The diameter is equal to 2 times the radius, while the circumference is equal to 2π times the radius. Therefore, the diameter is half the circumference.

**Question 4: The table we have to sit at has a circumference of 6.28 yards. We need to find the diameter of the table.**

A. 1 yard

B. 2 yards

C. 3 yards

D. 4 yards

✅ **Correct Answer:**

B. 2 yards

**Explanation:**

The circumference of a circle is calculated by multiplying the diameter by pi (π). In this case, the circumference is given as 6.28 yards. To find the diameter, we need to divide the circumference by pi. Dividing 6.28 yards by pi gives us approximately 2 yards. Therefore, the diameter of the table is 2 yards.

**Question 5: A circular garden has a circumference of 36 meters. What is the approximate radius of the garden?**

A. 3.14 meters

B. 6 meters

C. 9 meters

D. 18 meters

✅ **Correct Answer:**

C. 9 meters

**Explanation:**

To find the radius, use the formula for circumference: C = 2πr. Rearrange the formula to solve for the radius: r = C / (2π). Plugging in the given circumference of 36 meters and using an approximate value of π as 3.14, you get r = 36 / (2 * 3.14) ≈ 9 meters.

**Question 6: A circular swimming pool has a radius of 8 meters. What is the approximate distance a swimmer travels around the pool when completing one lap?**

A. 16 meters

B. 25 meters

C. 50 meters

D. 100 meters

✅ **Correct Answer:**

C. 50 meters

**Explanation:**

To find the distance a swimmer travels around the pool for one lap, you use the circumference formula (C = 2πr). In this case, it's 2 * 3.14 * 8 meters ≈ 50.24 meters, which is approximately 50 meters.

Question 7: When measuring the hula hoop in class, group C discovered that it had a radius of 7 inches. What is the circumference of the hula hoop?

A. 39.6 inches

B. 37.6 inches

C. 47.6 inches

D. 49.6 inches

✅ **Correct Answer:**

C. 47.6 inches

**Explanation:**

The circumference of a circle can be found using the formula C = 2πr, where r is the radius of the circle. In this case, the radius of the hula hoop is given as 7 inches. Plugging this value into the formula, we get C = 2π(7) = 14π inches. Approximating π to 3.14, we can calculate the circumference as 14(3.14) = 43.96 inches. Rounded to the nearest tenth, the circumference is 47.6 inches, which matches the given answer.

**Question 8: A semicircle has a radius of 10 meters. What is its perimeter?**

A. 20 meters

B. 15 meters

C. 31.42 meters

D. 62.84 meters

✅ **Correct Answer:**

C. 31.42 meters

**Explanation:** To find the perimeter of the semicircle, calculate half the circumference of a full circle with a radius of 10 meters.

**Question 9: The basketball team plays with a ball with a radius of 5.6 inches. What is the circumference of each basketball?**

A. 11.2 inches

B. 17.6 inches

C. 22.4 inches

D. 35.2 inches

✅ **Correct Answer:**

C. 22.4 inches

**Explanation**:

You can use the formula for the circumference of a circle, which is C = 2πr. The given radius is 5.6 inches. Plug this value into the formula, we have C = 2π * 5.6 inches. C ≈ 2 * 3.14 * 5.6 inches. C ≈ 11.2 * 5.6 inches. C ≈ 22.4 inches. So, the circumference of each basketball is approximately 22.4 inches. This represents the distance around the basketball.

**Question 10: Sarah and her two friends were building a circular picnic table for their gathering. They knew that in order for all of them to comfortably sit around the table, they needed a circumference of 18 feet. What diameter must the picnic table have to achieve the correct circumference?**

A. 3 feet

B. 6 feet

C. 9 feet

D. 12 feet

✅ **Correct Answer:**

B. 6 feet

**Explanation:**

To find the radius, divide the circumference by 2π, we have r = C / (2π) r = 18 feet / (2 * 3.14) r ≈ 18 feet / 6.28 r ≈ 2.87 feet (rounded to the nearest hundredth).

Now, to find the diameter, simply double the radius: Diameter = 2 * Radius Diameter ≈ 2 * 2.87 feet Diameter ≈ 5.74 feet. So, the picnic table must have a diameter of approximately 5.74 feet

## Key takeaways

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## Frequently Asked Questions

**What is 2πr of a circle?**

2πr is the formula for the circumference of a circle. In this formula:

- "2" represents that you are taking twice the length of the radius. The circumference is the distance around the circle, so you need to go around the circle once and then again, which is why we multiply by 2.
- "π" (pi) is a mathematical constant approximately equal to 3.14159. It's used because it represents the relationship between the circumference and the diameter of a circle.
- "r" represents the radius of the circle, which is the distance from the center of the circle to any point on its circumference.

**Why circumference is 2πr?**

The formula for the circumference of a circle, C = 2πr, comes from the definition of pi (π) and the geometric properties of a circle. Pi (π) represents the ratio of the circumference of a circle to its diameter. When you multiply the radius (r) by 2π, you essentially calculate the distance around the circle, which is the definition of circumference.

**Is the circumference 3.14 times the radius?**

No, the circumference is not exactly 3.14 times the radius. The relationship between the circumference and the radius of a circle is given by the formula C = 2πr. While π (pi) is approximately 3.14159, the circumference is 2 times π times the radius. So, the circumference is more than just 3.14 times the radius; it's 2 times π times the radius.

Ref: Omni Caculator | Proprof