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Chapter 6: Problem 6

Find the radius of each circle with the given diameter. $$d=4.8 \mathrm{cm}$$

Short Answer

Expert verified
The radius is 2.4 cm.

Step by step solution

01

Understand the relationship

The radius of a circle is half of its diameter. This relationship can be expressed with the formula: \[ r = \frac{d}{2} \] where \( r \) is the radius and \( d \) is the diameter.
02

Apply the formula

Substitute the given diameter into the formula: \[ r = \frac{4.8 \text{ cm}}{2} \]
03

Calculate the radius

Divide the diameter by 2: \[ r = \frac{4.8 \text{ cm}}{2} = 2.4 \text{ cm} \]

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Key Concepts

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

Circle Diameter Calculation
The diameter of a circle is a straight line that passes through the center and touches both sides of the circle. It is essentially twice the length of the radius. This means if you know the diameter, you can easily find the radius by simply dividing the diameter by 2.

In our exercise, the given diameter was 4.8 cm. By applying the formula for radius calculation, we were able to find out that the radius is 2.4 cm. Understanding this relationship helps lay the groundwork for solving problems related to the geometrical properties of circles.

Remember, the diameter is always twice as long as the radius.
Radius Formula Explanation
The radius of a circle is a line from the center of the circle to any point on its edge. The basic formula connecting the radius (\r\text) and the diameter (\r\text) is: \r\text \( r = \frac{d}{2} \).

This formula makes it simple to find the radius if the diameter is given, and vice versa.

For example, if a circle has a diameter of 4.8 cm, substitute that value into the radius formula:

\r\text \( r =\frac{ 4.8 \text{ cm}}{2}\)

When you divide 4.8 cm by 2, you get:

\r\text \( r = 2.4 \text{ cm } \)

So, the radius of the circle is 2.4 cm. This straightforward calculation is very useful in basic geometry, where you often encounter circles.
Understanding Basic Geometry
Basic geometry forms the foundation for understanding shapes, sizes, and the properties of space. One of the first concepts you encounter is the circle, along with its key elements: the radius and the diameter.

Key points to remember about circles include:
  • The circle's diameter is twice as long as its radius.
  • The radius is a line segment from the center to any point on the edge.
  • The diameter passes through the center and touches two points on the edge.
Understanding these basic properties can help you tackle more complex geometry problems in the future. Moreover, it helps you develop a sense of spatial awareness and accuracy in measurements. In our example, finding the circle's radius from the diameter is a fundamental application of these basic geometry principles.

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Most popular questions from this chapter

A classmate says the endpoints of any diameter of a circle are also endpoints of a semicircle. Do you agree? Explain your reasoning.

The length of any chord in a circle is less than or equal to the length of a diameter.

How far is a \(12 \mathrm{cm}\) chord from the center of a circle with diameter \(20 \mathrm{cm} ?\)

Find the diameter of each circle with the given radius. $$r=13.25 \mathrm{yd}$$

If \(\angle A\) and \(\angle B\) are two central angles in a circle with \(m \angle A>m \angle B\), then the arc intercepted by \(\angle A\) is greater than the arc intercepted by \(\angle B\).
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