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Chapter 0: Problem 7

Find the circumference of a circle with radius \(4 \mathrm{ft}\).

Short Answer

Expert verified
\(8 \pi \text{ft}\)

Step by step solution

01

Recall the Formula for Circumference

The formula to find the circumference of a circle is given by \(C = 2 \pi r\), where \(r\) is the radius of the circle.
02

Substitute the Given Radius into the Formula

Here, the radius \(r\) is \(4 \mathrm{ft}\). Substitute \(4 \mathrm{ft}\) into the formula: \[C = 2 \pi \(4 \text{ft}\)\].
03

Simplify the Equation

Simplify the equation: \[C = 2 \pi \(4 \text{ft}\) = 8 \pi \text{ft}\].

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Key Concepts

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

radius
The radius of a circle is the distance from its center to any point on its edge. It is half of the diameter, which is the distance across the circle through its center.
The radius is crucial because it helps us find other properties of the circle, such as its circumference and area.
In this exercise, the radius is given as 4 feet. Remember, the radius can be any positive number, and it is always measured in the same units as the circumference and area.
circumference formula
The circumference of a circle is the distance around it. We can find it using the formula: \(C = 2 \pi r\), where:
  • \(C\) stands for circumference
  • \(\pi\) is a constant approximately equal to 3.14159
  • \(r\) is the radius of the circle
Using this formula, we can determine the circumference when we know the radius.
For this specific example, the radius is 4 feet, so we substitute it into the formula:
\[C = 2 \pi * 4 \text{ft}\]This simplifies to:
\[C = 8 \pi \text{ft}\]
simplifying equations
Simplifying equations involves reducing them to their simplest form. This can include combining like terms or using basic arithmetic operations.
In the context of our exercise, we start with:
\[C = 2 \pi * 4 \text{ft}\]We then multiply the constants and the radius:
\[C = 8 \pi \text{ft}\]This step-by-step simplification is crucial as it reduces the problem to a more understandable form. It also helps ensure accuracy in larger, more complex calculations.
Simplifying equations makes solving problems more manageable and ensures we get the correct results.

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Most popular questions from this chapter

Use the formulas given in this section to compute the total surface area and the volume of the figure described. All answers should be rounded to the nearest tenth. A closed right circular cylinder of height \(5 \mathrm{cm}\) and radius \(4 \mathrm{cm}\)

A side of one triangle is 28 in. and the corresponding side of a second similar triangle is 42 in... If the perimeter of the first triangle is 98 in. and its area is \(420 \mathrm{sq}\) in.., find the perimeter and area of the similar triangle.

Find the perimeter and area of a rectangle with base \(9 \mathrm{cm}\) and height \(8 \mathrm{cm} .\)

Find the length of the diagonal of a square with side 8 in.

Will a 15 -in. ruler fit in an \(8 \frac{1}{2}\) - by 11 -in. envelope? Explain your answer. (Assume that the width of the ruler is negligible.)
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