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Chapter 6: Problem 2

Find the diameter of each circle with the given radius. $$r=5.8 \mathrm{cm}$$

Short Answer

Expert verified
The diameter is 11.6 cm.

Step by step solution

01

Understand the relationship between radius and diameter

The diameter of a circle is twice the length of its radius. Mathematically, this is expressed as \(d = 2r\).
02

Substitute the given radius

Substitute the given radius value into the formula. Here, the radius \(r = 5.8 \mathrm{cm}\). So, we have \(d = 2 \times 5.8\mathrm{cm}\).
03

Perform the multiplication

Multiply the radius by 2 to find the diameter: \(d = 2 \times 5.8 = 11.6 \mathrm{cm}\).

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Key Concepts

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

radius and diameter relationship
In circle geometry, the terms 'radius' and 'diameter' are fundamental.
The radius of a circle is the distance from the circle's center to any point on its edge.
The diameter is the distance across the circle, passing through the center.
A crucial relationship to remember is that the diameter is twice the length of the radius.
This relationship is expressed with the formula: \(d = 2r\).
This means if you know the radius, you can easily find the diameter by multiplying the radius by 2.
It鈥檚 a direct and simple calculation that's vital for solving many problems in circle geometry.
diameter calculation
Calculating the diameter of a circle is straightforward once you know the radius.
Let's use the given exercise as an example: the radius \(r = 5.8 \mathrm{cm}\).
To find the diameter, apply the formula \(d = 2r\).
We can substitute the given radius into the formula:
\(d = 2 \times 5.8 \mathrm{cm}\)
When you perform this multiplication, you get \(d = 11.6 \mathrm{cm}\).
This result demonstrates how knowing just one property of a circle (the radius) can allow you to find another key property (the diameter).
basic multiplication in geometry
Basic multiplication skills are essential in geometry, especially when working with circles.
As seen in the exercise, we used simple multiplication to solve for the diameter from a known radius.
Here鈥檚 a quick way to remember the process:
  • Identify the radius of the circle.
  • Recall the relationship between radius and diameter: \(d = 2r\).
  • Substitute the given radius into the formula.
  • Multiply the radius by 2 to find the diameter.

Practicing these steps helps reinforce both multiplication and understanding of circle properties.
The operations are simple but pack a lot of importance in solving geometry problems efficiently.

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