The sphere has a radius of 4 cm

Oct 13, 2025 by thesweetdesigns.com 45 views

Introduction

When dealing with spheres, it's essential to understand the relationship between the diameter and the radius. The diameter is the distance across the sphere passing through its center, while the radius is the distance from the center to any point on the sphere's surface. In this article, we'll explore the relationship between the diameter and the radius of a sphere with a diameter of 8 cm and determine which statements about the sphere are true.

Understanding the Relationship Between Diameter and Radius

The relationship between the diameter and the radius of a sphere is straightforward. The diameter is twice the length of the radius. This means that if you know the diameter of a sphere, you can easily calculate its radius by dividing the diameter by 2.

Statement 1: The sphere has a radius of 4 cm

To determine if this statement is true, we need to calculate the radius of the sphere using the given diameter. Since the diameter is 8 cm, we can divide it by 2 to get the radius.

diameter = 8 cm
radius = diameter / 2
radius = 4 cm

As we can see, the radius of the sphere is indeed 4 cm. Therefore, Statement 1: The sphere has a radius of 4 cm is true.

Statement 2: The sphere has a radius of 16 cm

To determine if this statement is true, we need to calculate the radius of the sphere using the given diameter. Since the diameter is 8 cm, we can divide it by 2 to get the radius.

diameter = 8 cm
radius = diameter / 2
radius = 4 cm

As we can see, the radius of the sphere is not 16 cm, but rather 4 cm. Therefore, Statement 2: The sphere has a radius of 16 cm is false.

Statement 3: The diameter's length is twice the length of the radius

This statement is a general property of spheres. The diameter is indeed twice the length of the radius. Since we've already established that the radius of the sphere is 4 cm, we can calculate the diameter by multiplying the radius by 2.

radius = 4 cm
diameter = radius * 2
diameter = 8 cm

As we can see, the diameter of the sphere is indeed 8 cm, which is twice the length of the radius. Therefore, Statement 3: The diameter's length is twice the length of the radius is true.

Conclusion

In conclusion, the statements about the sphere are true are:

The sphere has a radius of 4 cm
The diameter's length is twice the length of the radius

The statements that are false are:

The sphere has a radius of 16 cm

By understanding the relationship between the diameter and the radius of a sphere, we can easily determine which statements about the sphere are true.

Frequently Asked Questions

Q: What is the relationship between the diameter and the radius of a sphere?

A: The diameter of a sphere is twice the length of the radius.

Q: How can I calculate the radius of a sphere if I know its diameter?

A: To calculate the radius of a sphere, you can divide the diameter by 2.

Q: What is the diameter of a sphere with a radius of 4 cm?

A: The diameter of a sphere with a radius of 4 cm is 8 cm.

Final Thoughts

In this article, we've explored the relationship between the diameter and the radius of a sphere with a diameter of 8 cm. We've determined which statements about the sphere are true and which are false. By understanding the relationship between the diameter and the radius of a sphere, we can easily calculate the radius of a sphere if we know its diameter.

Introduction

Understanding the Relationship Between Diameter and Radius

Statement 1: The sphere has a radius of 4 cm

To determine if this statement is true, we need to calculate the radius of the sphere using the given diameter. Since the diameter is 8 cm, we can divide it by 2 to get the radius.

diameter = 8 cm
radius = diameter / 2
radius = 4 cm

As we can see, the radius of the sphere is indeed 4 cm. Therefore, Statement 1: The sphere has a radius of 4 cm is true.

Statement 2: The sphere has a radius of 16 cm

To determine if this statement is true, we need to calculate the radius of the sphere using the given diameter. Since the diameter is 8 cm, we can divide it by 2 to get the radius.

diameter = 8 cm
radius = diameter / 2
radius = 4 cm

As we can see, the radius of the sphere is not 16 cm, but rather 4 cm. Therefore, Statement 2: The sphere has a radius of 16 cm is false.

Statement 3: The diameter's length is twice the length of the radius

radius = 4 cm
diameter = radius * 2
diameter = 8 cm

As we can see, the diameter of the sphere is indeed 8 cm, which is twice the length of the radius. Therefore, Statement 3: The diameter's length is twice the length of the radius is true.

Conclusion

In conclusion, the statements about the sphere are true are:

The sphere has a radius of 4 cm
The diameter's length is twice the length of the radius

The statements that are false are:

The sphere has a radius of 16 cm

By understanding the relationship between the diameter and the radius of a sphere, we can easily determine which statements about the sphere are true.

Frequently Asked Questions

Q: What is the relationship between the diameter and the radius of a sphere?

A: The diameter of a sphere is twice the length of the radius.

Q: How can I calculate the radius of a sphere if I know its diameter?

A: To calculate the radius of a sphere, you can divide the diameter by 2.

Q: What is the diameter of a sphere with a radius of 4 cm?

A: The diameter of a sphere with a radius of 4 cm is 8 cm.

Q: What is the radius of a sphere with a diameter of 8 cm?

A: The radius of a sphere with a diameter of 8 cm is 4 cm.

Q: Is the statement "The sphere has a radius of 16 cm" true or false?

A: The statement "The sphere has a radius of 16 cm" is false.

Q: Is the statement "The diameter's length is twice the length of the radius" true or false?

A: The statement "The diameter's length is twice the length of the radius" is true.

Q: How can I determine which statements about a sphere are true or false?

A: To determine which statements about a sphere are true or false, you can use the relationship between the diameter and the radius of a sphere. If the statement is consistent with this relationship, it is true. Otherwise, it is false.

Final Thoughts

Additional Resources

Conclusion

In conclusion, the relationship between the diameter and the radius of a sphere is a fundamental concept in geometry. By understanding this relationship, we can easily determine which statements about a sphere are true or false. We hope this article has been helpful in understanding this concept.