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Chapter 0: Problem 5

Find the circumference of a circle with diameter 6 in.

Short Answer

Expert verified
The circumference is approximately 18.85 inches.

Step by step solution

01

Identify the formula for circumference

The formula to find the circumference of a circle is given by \ C = \pi \times d \ where \( C \) is the circumference and \( d \) is the diameter.
02

Substitute the diameter into the formula

Given that the diameter \( d \) is 6 inches, substitute this value into the formula: \ C = \pi \times 6 \
03

Calculate the circumference

Now, calculate the circumference: \ C = 6\pi \approx 18.85 \ inches, using \( \pi \approx 3.14159 \).

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Key Concepts

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

geometry formulas
Understanding geometry formulas is essential in solving many problems related to shapes and figures. One such formula is used to find the circumference of a circle. The circumference is the distance around the edge of the circle. For a circle, this is calculated using the formula: \( C = \pi \times d \). Here, \( C \) represents the circumference and \( d \) stands for the diameter. Another common geometry formula related to circles is the area formula, \( A = \pi r^2 \), where \( A \) denotes the area and \( r \) is the radius of the circle.
diameter and circumference relationship
The diameter and circumference of a circle are closely related. The diameter is the straight line passing from one side of the circle to the other through the center point. Essentially, it is twice the radius of the circle. The relationship between diameter and circumference is crucial; the circumference is calculated by multiplying the diameter by \( \pi \). This means that for every unit increase in the diameter, the circumference increases by approximately \( 3.14159 \) times that unit. For example, in the given exercise, the diameter is 6 inches, so the circumference becomes \( 6 \times \pi \), which is approximately 18.85 inches.
蟺 (pi) value
Pi (\( \pi \)) is a special mathematical constant that represents the ratio of the circumference of a circle to its diameter. Its value is approximately 3.14159. Pi is an irrational number, which means it cannot be expressed exactly as a simple fraction and its decimal representation never ends or repeats. In many calculations, \( \pi \) is often approximated to 3.14 for simplicity, but more precise values like 3.14159 or the fraction \( 22/7 \) are also commonly used. Understanding the value of \( \pi \) and how it is used helps in solving various problems involving circles, such as finding the circumference or area.

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Most popular questions from this chapter

Find the length of the sides of a rhombus with diagonals \(12^{\prime \prime}\) and \(18^{\prime \prime}\).

Find the circumference of a circle with diameter \(8 \mathrm{cm} .\)

Find the area of a sector with a central angle of \(80^{\circ}\) and a radius of 5 in.

Find the area of a circle with radius \(8 \mathrm{cm}\)

In Exercises \(21-26,\) round your answer to the nearest tenth where necessary. A scale model of an airplane uses a scale of \(\frac{1}{40} .\) If the model exhibits a wingspan of 8 in., what is the actual wingspan of the plane?
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