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Chapter 1: Problem 7

Find the circumference of a circle with a diameter of \(6 \mathrm{~cm}\).

Short Answer

Expert verified
The circumference is 18.84 cm.

Step by step solution

01

Understand the formula for circumference

The formula for finding the circumference of a circle when the diameter is known is given by: \[ C = \pi \times d \] where \( C \) is the circumference and \( d \) is the diameter.
02

Identify the given values

In this problem, the diameter \( d \) of the circle is given as \( 6 \,\text{cm} \).
03

Substitute the given values into the formula

Substitute the given diameter into the formula and calculate the circumference: \[ C = \pi \, \times 6 \text{cm} \]
04

Calculate the circumference

Using the approximation \( \pi \ \approx 3.14 \), we can calculate the circumference: \[ C = 3.14 \, \times 6 \text{cm} = 18.84 \text{cm} \]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

circumference formula
To find the circumference of a circle, you need to use a special formula. The formula is very straightforward: \[ C = \pi \times d \]
This formula tells us that the circumference (\( C \)) of a circle is equal to Pi (\( \pi \)) multiplied by the diameter (\( d \)).
Understanding this formula is essential because it helps to calculate the outer boundary length of any circle if you know the diameter.
diameter of a circle
The diameter of a circle is a line that passes from one side of the circle to the other, right through the center. It is twice as long as the radius, which stretches from the center to any point on the circle's edge.
If you know the diameter, you can easily proceed to find the circumference using the formula mentioned earlier. For example, if the diameter is given as \( 6 \,\text{cm} \), you can plug this value directly into the circumference formula.
pi approximation
Pi (\( \pi \)) is a special number in mathematics. It is the ratio of the circumference of a circle to its diameter. Although Pi is an irrational number and its exact value is infinite, we often use approximate values for practical calculations.
A common approximation of Pi is 3.14. By using this approximation, we can simplify our calculations, even though activities like engineering or advanced mathematics might use more precise values such as 3.14159 or others.
circle calculations
Once you understand the formula and have the values, performing the calculation is simple. Here鈥檚 a quick review of our example:
  • First, identify the diameter, which is \( 6 \,\text{cm} \).
  • Then use the formula for circumference: \( C = \pi \times d \).
  • Substitute \( \pi \approx 3.14 \) and \( d = 6 \text{cm} \).
  • Do the math: \( C = 3.14 \times 6 \text{cm} = 18.84 \text{cm} \).
This result, \( 18.84 \text{cm} \), is the distance around the circle. By mastering these steps, you can tackle any problem involving the circumference of a circle efficiently.

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Most popular questions from this chapter

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\( 3^{3}\)

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