Understanding the Diameter and Radius of the Sphere

Oct 13, 2025 by vinooalluri.com 149 views

Introduction

When dealing with spheres, it's essential to understand the relationship between the diameter, radius, and surface area. The given problem involves a sphere with a diameter of 8 cm, and we need to determine which statements about the sphere are true. To solve this problem, we'll use the formula for the surface area of a sphere, which is $S A = 4 \pi r^2$ . In this article, we'll explore the properties of the sphere, calculate its surface area, and determine the correct statements about the sphere.

Understanding the Diameter and Radius of the Sphere

The diameter of a sphere is twice the radius. Given that the diameter of the sphere is 8 cm, we can calculate the radius by dividing the diameter by 2.

diameter = 8  # in cm
radius = diameter / 2
print(radius)  # Output: 4.0

So, the radius of the sphere is 4 cm. This means that statement A, "The sphere has a radius of 4 cm," is true.

Calculating the Surface Area of the Sphere

Now that we know the radius of the sphere, we can use the formula $S A = 4 \pi r^2$ to calculate the surface area.

import math
radius = 4  # in cm
surface_area = 4 * math.pi * (radius ** 2)
print(surface_area)  # Output: 201.06192982974676

The surface area of the sphere is approximately 201.06 square centimeters.

Evaluating Statement B

Statement B claims that the sphere has a radius of 16 cm. However, we've already calculated the radius to be 4 cm. Therefore, statement B is false.

Conclusion

In conclusion, we've determined that the sphere has a radius of 4 cm and a surface area of approximately 201.06 square centimeters. The correct statements about the sphere are:

The sphere has a radius of 4 cm.
The surface area of the sphere is approximately 201.06 square centimeters.

Frequently Asked Questions

Q: What is the formula for the surface area of a sphere?

A: The formula for the surface area of a sphere is $S A = 4 \pi r^2$ .

Q: How do you calculate the radius of a sphere given its diameter?

A: To calculate the radius of a sphere given its diameter, divide the diameter by 2.

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

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

Final Thoughts

In this article, we've explored the properties of a sphere with a diameter of 8 cm. We've calculated the radius and surface area of the sphere using the formula $S A = 4 \pi r^2$ . By understanding the relationship between the diameter, radius, and surface area of a sphere, we can make informed decisions and solve problems involving spheres.

Introduction

In our previous article, we explored the properties of a sphere with a diameter of 8 cm. We calculated the radius and surface area of the sphere using the formula $S A = 4 \pi r^2$ . In this article, we'll answer some frequently asked questions about spheres and provide additional information to help you better understand the properties and calculations involved.

Q&A

Q: What is the formula for the surface area of a sphere?

A: The formula for the surface area of a sphere is $S A = 4 \pi r^2$ .

Q: How do you calculate the radius of a sphere given its diameter?

A: To calculate the radius of a sphere given its diameter, divide the diameter by 2.

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

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

Q: What is the formula for the volume of a sphere?

A: The formula for the volume of a sphere is $V = \frac{4}{3} \pi r^3$ .

Q: How do you calculate the surface area of a sphere given its radius?

A: To calculate the surface area of a sphere given its radius, use the formula $S A = 4 \pi r^2$ .

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

A: The surface area of a sphere is directly proportional to the square of its radius.

Q: How do you calculate the volume of a sphere given its radius?

A: To calculate the volume of a sphere given its radius, use the formula $V = \frac{4}{3} \pi r^3$ .

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

A: The volume of a sphere is directly proportional to the cube of its radius.

Q: Can you provide an example of how to calculate the surface area and volume of a sphere?

A: Let's say we have a sphere with a radius of 5 cm. To calculate its surface area, we use the formula $S A = 4 \pi r^2$ :

import math
radius = 5  # in cm
surface_area = 4 * math.pi * (radius ** 2)
print(surface_area)  # Output: 314.1592653589793

To calculate its volume, we use the formula $V = \frac{4}{3} \pi r^3$ :

import math
radius = 5  # in cm
volume = (4/3) * math.pi * (radius ** 3)
print(volume)  # Output: 523.5987755982988

Q: What are some real-world applications of spheres?

A: Spheres have many real-world applications, including:

Balls: Spheres are used to make balls for sports, such as footballs, basketballs, and soccer balls.
Golf balls: Spheres are used to make golf balls, which are designed to fly through the air with a consistent trajectory.
Marbles: Spheres are used to make marbles, which are small balls used for play.
Space exploration: Spheres are used in space exploration to design spacecraft and satellites.
Medical imaging: Spheres are used in medical imaging to create 3D models of the body.

Conclusion

In this article, we've answered some frequently asked questions about spheres and provided additional information to help you better understand the properties and calculations involved. We've also provided examples of how to calculate the surface area and volume of a sphere, as well as discussed some real-world applications of spheres. By understanding the properties and calculations involved, you can make informed decisions and solve problems involving spheres.

Final Thoughts

Spheres are an important concept in mathematics and have many real-world applications. By understanding the properties and calculations involved, you can make informed decisions and solve problems involving spheres. Whether you're a student, a professional, or simply someone interested in learning more about spheres, this article has provided you with a comprehensive overview of the subject.