Diameter - Examples, Exercises and Solutions

Understanding Diameter

Complete explanation with examples

A diameter is a section that connects two points that lie on the circumference, that passes through the center of the circle. The diameter is actually twice the radius.

As in the case of the radius, as well as in the case of the diameter, there are an infinite number of diameters on the circumference, and all are identical in length.

Below is an example of a circle with several diameters marked in different colors.

Diameter

Detailed explanation

Practice Diameter

Test your knowledge with 11 quizzes

True or false:

The radius of a circle is the chord.

Examples with solutions for Diameter

Step-by-step solutions included
Exercise #1

There are only 4 radii in a circle.

Step-by-Step Solution

A radius is a straight line that connects the center of the circle with a point on the circle itself.

Therefore, the answer is incorrect, as there are infinite radii.

Answer:

False

Exercise #2

If the radius of a circle is 5 cm, then the length of the diameter is 10 cm.

Step-by-Step Solution

To determine if the statement "If the radius of a circle is 5 cm, then the length of the diameter is 10 cm" is true, we need to use the relationship between the radius and diameter of a circle.

The diameter d d of a circle is calculated using the formula:

d=2r d = 2r

where r r is the radius. In this problem, the radius r r is given as 5 cm.

Using the formula, the diameter is:

d=2×5cm=10cm d = 2 \times 5 \, \text{cm} = 10 \, \text{cm}

This matches exactly the length of the diameter given in the problem.

Therefore, the statement "If the radius of a circle is 5 cm, then the length of the diameter is 10 cm" is True.

Answer:

True

Exercise #3

The number Pi (π) (\pi) represents the relationship between which parts of the circle?

Step-by-Step Solution

To solve this problem, we will clarify the relationship between the constant π\pi and parts of a circle.

The number π\pi is a constant that relates the circumference of a circle (the perimeter) to its diameter. The formula for the circumference CC of a circle is given by:

C=π×d C = \pi \times d

where CC is the circumference, and dd is the diameter of the circle. This equation shows that π\pi is the ratio of the circumference of a circle to its diameter, which remains constant for all circles.

Therefore, π\pi indeed represents the relationship between the circle’s perimeter and its diameter.

Thus, the correct answer is: Perimeter and diameter

Answer:

Perimeter and diameter

Exercise #4

M is the center of the circle.

Perhaps AB=CD AB=CD

MMMAAABBBCCCDDDEEEFFFGGGHHH

Step-by-Step Solution

CD is a diameter, since it passes through the center of the circle, meaning it is the longest segment in the circle.

AB does not pass through the center of the circle and is not a diameter, therefore it is necessarily shorter.

Therefore:

ABCD AB\ne CD

Answer:

No

Video Solution
Exercise #5

Which diagram shows a circle with a point marked in the circle and not on the circle?

Step-by-Step Solution

The interpretation of "in a circle" is inside the circle.

In diagrams (a) and (d) the point is on the circle, while in diagram (c) the point is outside of the circle.

Answer:

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