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The volume of a sphere is a fundamental concept in mathematics and physics, and it has numerous applications in various fields. In this article, we will explore the formula for the volume of a sphere and use it to calculate the volume of a sphere with a given radius.

The Formula

The formula for the volume of a sphere is given by:

V = (4/3)πR^3

where V is the volume of the sphere, R is the radius of the sphere, and π is a mathematical constant approximately equal to 3.14.

Calculating the Volume

Now, let's use the formula to calculate the volume of a sphere with a radius of 6.8 cm. We will use the value 3.14 for π and round our answer to the nearest tenth.

Step 1: Plug in the values

First, we need to plug in the values of R and π into the formula:

V = (4/3)(3.14)(6.8)^3

Step 2: Calculate the cube of the radius

Next, we need to calculate the cube of the radius:

(6.8)^3 = 6.8 × 6.8 × 6.8 = 409.536

Step 3: Multiply the result by 4/3 and π

Now, we need to multiply the result by 4/3 and π:

(4/3)(3.14)(409.536) = 4.189 × 3.14 × 409.536 = 5381.059

Step 4: Round the result to the nearest tenth

Finally, we need to round the result to the nearest tenth:

V ≈ 5381.1

Therefore, the volume of the sphere with a radius of 6.8 cm is approximately 5381.1 cubic centimeters.

Conclusion

In this article, we have used the formula for the volume of a sphere to calculate the volume of a sphere with a given radius. We have plugged in the values of R and π into the formula, calculated the cube of the radius, multiplied the result by 4/3 and π, and rounded the result to the nearest tenth. The final answer is 5381.1 cubic centimeters.

References

Mathematics Handbook
Geometry and Trigonometry
Calculus

Glossary

Sphere: A three-dimensional shape with all points equidistant from a central point.
Radius: The distance from the center of a sphere to any point on its surface.
Volume: The amount of space inside a three-dimensional shape.
π: A mathematical constant approximately equal to 3.14.
The Formula for the Volume of a Sphere: Q&A =====================================================

In our previous article, we explored the formula for the volume of a sphere and used it to calculate the volume of a sphere with a given radius. In this article, we will answer some frequently asked questions about the formula for 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 given by:

V = (4/3)πR^3

where V is the volume of the sphere, R is the radius of the sphere, and π is a mathematical constant approximately equal to 3.14.

Q: What is the radius of a sphere?

A: The radius of a sphere is the distance from the center of the sphere to any point on its surface.

Q: What is the volume of a sphere?

A: The volume of a sphere is the amount of space inside the sphere.

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

A: To calculate the volume of a sphere, you need to plug in the values of R and π into the formula:

V = (4/3)(3.14)(R)^3

Then, you need to calculate the cube of the radius, multiply the result by 4/3 and π, and round the result to the nearest tenth.

Q: What is the value of π?

A: The value of π is a mathematical constant approximately equal to 3.14.

Q: Can I use a calculator to calculate the volume of a sphere?

A: Yes, you can use a calculator to calculate the volume of a sphere. Simply plug in the values of R and π into the formula and calculate the result.

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

A: The formula for the volume of a sphere has numerous real-world applications, including:

Calculating the volume of a ball or a sphere in a game or simulation
Determining the volume of a container or a tank
Calculating the volume of a sphere in a scientific experiment or study
Designing a sphere or a spherical object, such as a ball or a globe

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

A: No, the formula for the volume of a sphere is specific to spheres and cannot be used to calculate the volume of other shapes.

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 intermediate calculations
Using the wrong value of π
Forgetting to calculate the cube of the radius
Forgetting to multiply the result by 4/3 and π

Conclusion

In this article, we have answered some frequently asked questions about the formula for the volume of a sphere. We have covered topics such as the formula, the radius, the volume, and real-world applications. We hope that this article has been helpful in clarifying any questions you may have had about the formula for the volume of a sphere.

References

Mathematics Handbook
Geometry and Trigonometry
Calculus

Glossary

Sphere: A three-dimensional shape with all points equidistant from a central point.
Radius: The distance from the center of a sphere to any point on its surface.
Volume: The amount of space inside a three-dimensional shape.
π: A mathematical constant approximately equal to 3.14.