The Formula $V=\frac{4}{3} \pi R^3$ Gives The Volume $V$ Of A Sphere With Radius $r$. What Is The Volume, In Cubic Feet, Of A Sphere With A Radius Of 2 Feet?Choose 1 Answer:(A) $4 \pi$(B) $8
Introduction to the Formula
The formula for the volume of a sphere is a fundamental concept in mathematics, particularly in geometry. The formula, represented as $V=\frac{4}{3} \pi r^3$, calculates the volume of a sphere with a given radius. In this article, we will delve into the world of spheres and explore the calculation of the volume of a sphere with a radius of 2 feet.
Understanding the Formula
The formula for the volume of a sphere is derived from the concept of the sphere's geometry. The volume of a sphere is calculated by taking the product of the sphere's radius and the surface area of the sphere. The surface area of a sphere is given by the formula $A=4 \pi r^2$, where $r$ is the radius of the sphere. By substituting the surface area formula into the volume formula, we get $V=\frac{4}{3} \pi r^3$.
Calculating the Volume of a Sphere with a Radius of 2 Feet
To calculate the volume of a sphere with a radius of 2 feet, we can simply substitute the radius into the formula. The formula becomes $V=\frac{4}{3} \pi (2)^3$. By simplifying the equation, we get $V=\frac{4}{3} \pi (8)$.
Simplifying the Equation
To simplify the equation, we can multiply the numerator and denominator by 8. This gives us $V=\frac{32}{3} \pi$. Since we are asked to provide the answer in cubic feet, we can convert the answer to cubic feet by multiplying the answer by $\frac{1}{1}$.
Converting the Answer to Cubic Feet
To convert the answer to cubic feet, we can multiply the answer by $\frac{1}{1}$. This gives us $V=\frac{32}{3} \pi \times \frac{1}{1}$.
Final Answer
The final answer is $\frac{32}{3} \pi$ cubic feet.
Conclusion
In conclusion, the formula for the volume of a sphere is a fundamental concept in mathematics, particularly in geometry. By understanding the formula and applying it to a given radius, we can calculate the volume of a sphere. In this article, we calculated the volume of a sphere with a radius of 2 feet using the formula $V=\frac{4}{3} \pi r^3$. The final answer is $\frac{32}{3} \pi$ cubic feet.
Frequently Asked Questions
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 I calculate the volume of a sphere with a given radius?
A: To calculate the volume of a sphere with a given radius, you can substitute the radius into the formula and simplify the equation.
Q: What is the final answer for the volume of a sphere with a radius of 2 feet?
A: The final answer is $\frac{32}{3} \pi$ cubic feet.
Q: Can I convert the answer to cubic feet?
A: Yes, you can convert the answer to cubic feet by multiplying the answer by $\frac{1}{1}$.
References
- [1] Wikipedia. (2023). Sphere. Retrieved from https://en.wikipedia.org/wiki/Sphere
- [2] Math Open Reference. (2023). Volume of a sphere. Retrieved from https://www.mathopenref.com/spherevolume.html
Discussion
- What is the formula for the volume of a sphere?
- How do I calculate the volume of a sphere with a given radius?
- What is the final answer for the volume of a sphere with a radius of 2 feet?
- Can I convert the answer to cubic feet?
Related Topics
- Geometry
- Mathematics
- Formula for the volume of a sphere
- Calculating the volume of a sphere
- Converting the answer to cubic feet
Introduction
In our previous article, we explored the formula for the volume of a sphere, which is given by $V=\frac{4}{3} \pi r^3$. We also calculated the volume of a sphere with a radius of 2 feet using this formula. In this article, we will answer some frequently asked questions related to the formula for the volume of a sphere.
Q&A
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 I calculate the volume of a sphere with a given radius?
A: To calculate the volume of a sphere with a given radius, you can substitute the radius into the formula and simplify the equation.
Q: What is the final answer for the volume of a sphere with a radius of 2 feet?
A: The final answer is $\frac{32}{3} \pi$ cubic feet.
Q: Can I convert the answer to cubic feet?
A: Yes, you can convert the answer to cubic feet by multiplying the answer by $\frac{1}{1}$.
Q: What is the significance of the $\pi$ symbol in the formula?
A: The $\pi$ symbol represents the mathematical constant pi, which is approximately equal to 3.14159. The $\pi$ symbol is used in the formula to represent the ratio of the circumference of a circle to its diameter.
Q: Can I use the formula to calculate the volume of a sphere with a negative radius?
A: No, you cannot use the formula to calculate the volume of a sphere with a negative radius. The radius of a sphere is always a positive value.
Q: Can I use the formula to calculate the volume of a sphere with a radius of zero?
A: Yes, you can use the formula to calculate the volume of a sphere with a radius of zero. In this case, the volume of the sphere is zero.
Q: Can I use the formula to calculate the volume of a sphere with a radius that is not a whole number?
A: Yes, you can use the formula to calculate the volume of a sphere with a radius that is not a whole number. For example, you can calculate the volume of a sphere with a radius of 2.5 feet.
Q: Can I use the formula to calculate the volume of a sphere with a radius that is a fraction?
A: Yes, you can use the formula to calculate the volume of a sphere with a radius that is a fraction. For example, you can calculate the volume of a sphere with a radius of $\frac{1}{2}$ feet.
Conclusion
In conclusion, the formula for the volume of a sphere is a fundamental concept in mathematics, particularly in geometry. By understanding the formula and applying it to a given radius, we can calculate the volume of a sphere. In this article, we answered some frequently asked questions related to the formula for the volume of a sphere.
Frequently Asked Questions
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 I calculate the volume of a sphere with a given radius?
A: To calculate the volume of a sphere with a given radius, you can substitute the radius into the formula and simplify the equation.
Q: What is the final answer for the volume of a sphere with a radius of 2 feet?
A: The final answer is $\frac{32}{3} \pi$ cubic feet.
Q: Can I convert the answer to cubic feet?
A: Yes, you can convert the answer to cubic feet by multiplying the answer by $\frac{1}{1}$.
References
- [1] Wikipedia. (2023). Sphere. Retrieved from https://en.wikipedia.org/wiki/Sphere
- [2] Math Open Reference. (2023). Volume of a sphere. Retrieved from https://www.mathopenref.com/spherevolume.html
Discussion
- What is the formula for the volume of a sphere?
- How do I calculate the volume of a sphere with a given radius?
- What is the final answer for the volume of a sphere with a radius of 2 feet?
- Can I convert the answer to cubic feet?
Related Topics
- Geometry
- Mathematics
- Formula for the volume of a sphere
- Calculating the volume of a sphere
- Converting the answer to cubic feet