Incorrect calculation of the cube of the radius

Oct 13, 2025 by magicalceylontours.com 81 views

Introduction

In mathematics, the volume of a sphere is a fundamental concept that is used to calculate the amount of space inside a sphere. The formula for the volume of a sphere is given by V = (4/3)πr^3, where V is the volume and r is the radius of the sphere. In this article, we will use the given radius of 1.5 inches and the value of pi as 3.14 to calculate the volume of the sphere.

Understanding the Formula

The formula for the volume of a sphere is V = (4/3)πr^3. This formula is derived from the concept of integration and is used to calculate the volume of a sphere. The formula consists of three main components:

4/3: This is a constant that is used to calculate the volume of a sphere.
π: This is a mathematical constant that is approximately equal to 3.14.
r^3: This is the cube of the radius of the sphere.

Calculating the Volume

To calculate the volume of the sphere, we need to substitute the given values into the formula. The given radius of the sphere is 1.5 inches and the value of pi is 3.14. Substituting these values into the formula, we get:

V = (4/3) × 3.14 × (1.5)^3

Step 1: Calculate the Cube of the Radius

The first step is to calculate the cube of the radius. The radius of the sphere is 1.5 inches, so we need to calculate (1.5)^3.

(1.5)^3 = 1.5 × 1.5 × 1.5 = 3.375

Step 2: Multiply the Constant and Pi

The next step is to multiply the constant (4/3) and pi (3.14).

(4/3) × 3.14 = 4.188

Step 3: Multiply the Results

The final step is to multiply the results of the previous two steps.

4.188 × 3.375 = 14.1025

Rounding the Result

The final result is 14.1025 cubic inches. However, we need to round this result to the nearest tenth. Rounding 14.1025 to the nearest tenth gives us 14.1 cubic inches.

Conclusion

In this article, we calculated the volume of a sphere with a radius of 1.5 inches using the formula V = (4/3)πr^3. We substituted the given values into the formula and calculated the result. The final result was 14.1 cubic inches, which is the correct answer.

Answer

The correct answer is B. 14.1 in^3.

Additional Information

The volume of a sphere is an important concept in mathematics and is used in a variety of applications, including physics, engineering, and computer science. The formula for the volume of a sphere is V = (4/3)πr^3, where V is the volume and r is the radius of the sphere. This formula is used to calculate the amount of space inside a sphere and is an essential concept in mathematics.

Real-World Applications

The volume of a sphere has a variety of real-world applications, including:

Physics: The volume of a sphere is used to calculate the amount of space inside a sphere, which is an important concept in physics.
Engineering: The volume of a sphere is used to calculate the amount of space inside a sphere, which is an important concept in engineering.
Computer Science: The volume of a sphere is used to calculate the amount of space inside a sphere, which is an important concept in computer science.

Conclusion

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

A: The formula for the volume of a sphere is V = (4/3)πr^3, where V is the volume and r is the radius of the sphere.

Q: What is the value of pi (π) used in the formula?

A: The value of pi (π) used in the formula is approximately 3.14.

Q: How do I calculate the cube of the radius?

A: To calculate the cube of the radius, you need to multiply the radius by itself three times. For example, if the radius is 1.5 inches, the cube of the radius is (1.5)^3 = 1.5 × 1.5 × 1.5 = 3.375.

Q: How do I multiply the constant and pi?

A: To multiply the constant and pi, you need to multiply 4/3 by 3.14. This gives you 4.188.

Q: How do I multiply the results?

A: To multiply the results, you need to multiply the result of the previous step by the cube of the radius. For example, if the result of the previous step is 4.188 and the cube of the radius is 3.375, the final result is 4.188 × 3.375 = 14.1025.

Q: How do I round the result to the nearest tenth?

A: To round the result to the nearest tenth, you need to look at the hundredth place digit. If the hundredth place digit is 5 or greater, you need to round up. If the hundredth place digit is less than 5, you need to round down. In this case, the hundredth place digit is 2, so you need to round down to 14.1.

Q: What are some real-world applications of the volume of a sphere?

A: The volume of a sphere has a variety of real-world applications, including:

Physics: The volume of a sphere is used to calculate the amount of space inside a sphere, which is an important concept in physics.
Engineering: The volume of a sphere is used to calculate the amount of space inside a sphere, which is an important concept in engineering.
Computer Science: The volume of a sphere is used to calculate the amount of space inside a sphere, which is an important concept in computer science.

Q: What are some common mistakes to avoid when calculating the volume of a sphere?

A: Some common mistakes to avoid when calculating the volume of a sphere include:

Rounding errors: Rounding errors can occur when you round the result to the nearest tenth. To avoid this, you need to make sure that you are rounding correctly.
Incorrect values of pi: Using an incorrect value of pi can affect the accuracy of the result. To avoid this, you need to use a reliable value of pi.
Incorrect calculation of the cube of the radius: Calculating the cube of the radius incorrectly can affect the accuracy of the result. To avoid this, you need to make sure that you are calculating the cube of the radius correctly.

Q: How can I practice calculating the volume of a sphere?

A: You can practice calculating the volume of a sphere by using online calculators or worksheets. You can also try calculating the volume of a sphere with different values of the radius to see how the result changes.

Conclusion

In conclusion, calculating the volume of a sphere is an important concept in mathematics that has a variety of real-world applications. By understanding the formula for the volume of a sphere and how to calculate it, you can apply this concept to a variety of situations. Remember to avoid common mistakes and practice calculating the volume of a sphere to become more confident in your calculations.