Rounding the Result to the Nearest Tenth of a Cubic Meter

Oct 13, 2025 by magicalceylontours.com 124 views

The volume of a sphere is a fundamental concept in mathematics, particularly in geometry. It is a crucial aspect of understanding the properties of three-dimensional objects. In this article, we will delve into the calculation of the volume of a sphere with a given radius and explore the significance of rounding the result to the nearest tenth of a cubic meter.

What is the Volume of a Sphere?

The volume of a sphere is given by the formula:

V = (4/3) * π * r^3

where V is the volume of the sphere, π is a mathematical constant approximately equal to 3.14159, and r is the radius of the sphere.

Calculating the Volume of a Sphere with a Radius of 6.7 m

To calculate the volume of a sphere with a radius of 6.7 m, we can plug the value of the radius into the formula:

V = (4/3) * π * (6.7)^3

Using a calculator or a computer program to evaluate the expression, we get:

V ≈ 1,163.19 cubic meters

Rounding the Result to the Nearest Tenth of a Cubic Meter

The problem asks us to round the result to the nearest tenth of a cubic meter. To do this, we need to examine the decimal part of the result. In this case, the decimal part is 0.19, which is less than 0.5. Therefore, we round down to the nearest tenth, which gives us:

V ≈ 1,163.2 cubic meters

Significance of Rounding the Result

Rounding the result to the nearest tenth of a cubic meter is a common practice in mathematics and engineering. It helps to simplify the result and make it easier to understand and work with. In many cases, the extra precision is not necessary, and rounding the result can provide a more accurate representation of the data.

Real-World Applications of the Volume of a Sphere

The volume of a sphere has numerous real-world applications in various fields, including:

Engineering: The volume of a sphere is used to calculate the volume of tanks, containers, and other vessels.
Architecture: The volume of a sphere is used to calculate the volume of domes, spheres, and other curved structures.
Physics: The volume of a sphere is used to calculate the volume of atoms, molecules, and other particles.

Conclusion

In conclusion, the volume of a sphere with a radius of 6.7 m is approximately 1,163.2 cubic meters, rounded to the nearest tenth of a cubic meter. The calculation of the volume of a sphere is a fundamental concept in mathematics, and it has numerous real-world applications in various fields. By understanding the volume of a sphere, we can better appreciate the properties of three-dimensional objects and make more accurate calculations in various fields.

Additional Resources

For those who want to learn more about the volume of a sphere, here are some additional resources:

Mathematics textbooks: There are many mathematics textbooks that cover the topic of the volume of a sphere.
Online resources: There are many online resources, such as Khan Academy and Mathway, that provide tutorials and examples on the volume of a sphere.
Engineering and architecture software: There are many software programs, such as Autodesk and SolidWorks, that can be used to calculate the volume of a sphere.

Frequently Asked Questions

Here are some frequently asked questions about the volume of a sphere:

What is the formula for the volume of a sphere?
- The formula for the volume of a sphere is V = (4/3) * π * r^3.
How do I calculate the volume of a sphere with a given radius?
- To calculate the volume of a sphere with a given radius, plug the value of the radius into the formula and evaluate the expression.
Why do I need to round the result to the nearest tenth of a cubic meter?
- Rounding the result to the nearest tenth of a cubic meter helps to simplify the result and make it easier to understand and work with.
  Frequently Asked Questions About the Volume of a Sphere =============================================================

In this article, we will answer some of the most frequently asked questions about the volume of a sphere.

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

A: The formula for the volume of a sphere is V = (4/3) * π * r^3, where V is the volume of the sphere, π is a mathematical constant approximately equal to 3.14159, and r is the radius of the sphere.

Q: How do I calculate the volume of a sphere with a given radius?

A: To calculate the volume of a sphere with a given radius, plug the value of the radius into the formula and evaluate the expression. For example, if the radius of the sphere is 6.7 m, the volume would be:

V = (4/3) * π * (6.7)^3

Using a calculator or a computer program to evaluate the expression, we get:

V ≈ 1,163.19 cubic meters

Q: Why do I need to round the result to the nearest tenth of a cubic meter?

A: Rounding the result to the nearest tenth of a cubic meter helps to simplify the result and make it easier to understand and work with. In many cases, the extra precision is not necessary, and rounding the result can provide a more accurate representation of the data.

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

A: The radius of the sphere is a critical component in the formula for the volume of a sphere. It determines the size of the sphere and, therefore, its volume. A larger radius results in a larger volume, while a smaller radius results in a smaller volume.

Q: Can I use the formula for the volume of a sphere to calculate the volume of a cylinder?

A: No, the formula for the volume of a sphere is not applicable to cylinders. The formula for the volume of a cylinder is V = π * r^2 * h, where V is the volume of the cylinder, π is a mathematical constant approximately equal to 3.14159, r is the radius of the cylinder, and h is the height of the cylinder.

Q: How do I calculate the volume of a sphere with a given diameter?

A: To calculate the volume of a sphere with a given diameter, you need to first find the radius of the sphere. The radius is half the diameter, so if the diameter is 13.4 m, the radius would be:

r = 13.4 / 2 = 6.7 m

Then, you can use the formula for the volume of a sphere to calculate the volume:

V = (4/3) * π * (6.7)^3

Using a calculator or a computer program to evaluate the expression, we get:

V ≈ 1,163.19 cubic meters

Q: Can I use the formula for the volume of a sphere to calculate the volume of a hemisphere?

A: Yes, you can use the formula for the volume of a sphere to calculate the volume of a hemisphere. A hemisphere is half a sphere, so the volume of a hemisphere is half the volume of a sphere. Therefore, if the radius of the sphere is 6.7 m, the volume of the hemisphere would be:

V = (1/2) * (4/3) * π * (6.7)^3

Using a calculator or a computer program to evaluate the expression, we get:

V ≈ 581.59 cubic meters

Q: How do I calculate the volume of a sphere with a given surface area?

A: To calculate the volume of a sphere with a given surface area, you need to first find the radius of the sphere. The surface area of a sphere is given by the formula A = 4 * π * r^2, where A is the surface area of the sphere and r is the radius of the sphere. Rearranging the formula to solve for the radius, we get:

r = √(A / (4 * π))

Then, you can use the formula for the volume of a sphere to calculate the volume:

V = (4/3) * π * (6.7)^3

Using a calculator or a computer program to evaluate the expression, we get:

V ≈ 1,163.19 cubic meters

Conclusion

In conclusion, the volume of a sphere is a fundamental concept in mathematics, and it has numerous real-world applications in various fields. By understanding the formula for the volume of a sphere and how to calculate it, you can better appreciate the properties of three-dimensional objects and make more accurate calculations in various fields.

Additional Resources

For those who want to learn more about the volume of a sphere, here are some additional resources:

Mathematics textbooks: There are many mathematics textbooks that cover the topic of the volume of a sphere.
Online resources: There are many online resources, such as Khan Academy and Mathway, that provide tutorials and examples on the volume of a sphere.
Engineering and architecture software: There are many software programs, such as Autodesk and SolidWorks, that can be used to calculate the volume of a sphere.