A Sphere Has A Radius Of 5 Inches. What Is Its Volume?Use The Formula For The Volume Of A Sphere: $ V = \frac{4}{3} \pi R^3 }$Substitute The Radius Into The Formula 1. Evaluate:${ V = \frac{4 {3} \pi (5)^3 }$2. Simplify The

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 ${ V = \frac{4}{3} \pi r^3 }$, where $r$ is the radius of the sphere. In this article, we will use this formula to calculate the volume of a sphere with a radius of 5 inches.

The Formula for the Volume of a Sphere

The formula for the volume of a sphere is given by ${ V = \frac{4}{3} \pi r^3 }$. This formula is derived from the fact that the volume of a sphere is proportional to the cube of its radius. The constant of proportionality is $\frac{4}{3} \pi$, which is a fundamental constant in mathematics.

Substituting the Radius into the Formula

To calculate the volume of a sphere with a radius of 5 inches, we need to substitute the radius into the formula. This is done by replacing $r$ with 5 in the formula:

{ V = \frac{4}{3} \pi (5)^3 \}

Evaluating the Expression

To evaluate the expression, we need to calculate the value of $(5)^3$. This is done by cubing 5, which gives us:

{ (5)^3 = 5 \times 5 \times 5 = 125 \}

Now, we can substitute this value back into the expression:

{ V = \frac{4}{3} \pi (125) \}

Simplifying the Expression

To simplify the expression, we need to multiply $\frac{4}{3} \pi$ by 125. This is done by multiplying the numerator and denominator of $\frac{4}{3} \pi$ by 125:

{ V = \frac{4}{3} \pi \times 125 = \frac{500}{3} \pi \}

Calculating the Value of $\pi$

To calculate the value of $\pi$, we can use the fact that $\pi$ is approximately equal to 3.14. We can substitute this value into the expression:

{ V = \frac{500}{3} \times 3.14 = \frac{1570}{3} \}

Calculating the Final Answer

To calculate the final answer, we need to divide 1570 by 3:

{ V = \frac{1570}{3} = 523.33 \}

Therefore, the volume of a sphere with a radius of 5 inches is approximately 523.33 cubic inches.

Conclusion

In this article, we used the formula for the volume of a sphere to calculate the volume of a sphere with a radius of 5 inches. We substituted the radius into the formula, evaluated the expression, simplified the expression, and calculated the final answer. The volume of a sphere with a radius of 5 inches is approximately 523.33 cubic inches.

Discussion

The formula for the volume of a sphere is a fundamental concept in mathematics that is used to calculate the amount of space inside a sphere. The formula is given by ${ V = \frac{4}{3} \pi r^3 }$, where $r$ is the radius of the sphere. In this article, we used this formula to calculate the volume of a sphere with a radius of 5 inches.

Related Topics

• Volume of a Cylinder: The volume of a cylinder is given by ${ V = \pi r^2 h }$, where $r$ is the radius of the cylinder and $h$ is the height of the cylinder.
• Surface Area of a Sphere: The surface area of a sphere is given by ${ A = 4 \pi r^2 }$, where $r$ is the radius of the sphere.
• Volume of a Cone: The volume of a cone is given by ${ V = \frac{1}{3} \pi r^2 h }$, where $r$ is the radius of the cone and $h$ is the height of the cone.

References

• Mathematics Handbook: A comprehensive handbook of mathematical formulas and theorems.
• Geometry and Trigonometry: A textbook on geometry and trigonometry that covers the basics of these subjects.
• Calculus: A textbook on calculus that covers the basics of this subject.

Further Reading

• Mathematics for Engineers: A textbook on mathematics for engineers that covers the basics of mathematics as applied to engineering.
• Mathematics for Scientists: A textbook on mathematics for scientists that covers the basics of mathematics as applied to science.
• Mathematics for Computer Scientists: A textbook on mathematics for computer scientists that covers the basics of mathematics as applied to computer science.
  Q&A: Calculating the Volume of a Sphere =============================================

Introduction

In our previous article, we calculated the volume of a sphere with a radius of 5 inches using the formula ${ V = \frac{4}{3} \pi r^3 }$. In this article, we will answer some frequently asked questions about calculating 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 ${ V = \frac{4}{3} \pi r^3 }$, where $r$ is the radius of the sphere.

Q: How do I calculate the volume of a sphere with a radius of 10 inches?

A: To calculate the volume of a sphere with a radius of 10 inches, you can substitute the radius into the formula:

{ V = \frac{4}{3} \pi (10)^3 \}

Evaluating the expression, we get:

{ V = \frac{4}{3} \pi (1000) = \frac{4000}{3} \pi \}

Using the value of $\pi$ as approximately 3.14, we get:

{ V = \frac{4000}{3} \times 3.14 = \frac{12640}{3} = 4213.33 \}

Therefore, the volume of a sphere with a radius of 10 inches is approximately 4213.33 cubic inches.

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

A: The volume of a sphere is proportional to the cube of its radius. This means that if the radius of a sphere is doubled, the volume of the sphere will increase by a factor of $2^3 = 8$.

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 the same as the formula for the volume of a cylinder. The formula for the volume of a cylinder is given by ${ V = \pi r^2 h }$, where $r$ 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 radius of 5 inches using a calculator?

A: To calculate the volume of a sphere with a radius of 5 inches using a calculator, you can enter the following values:

• Radius: 5
• Formula: ${ V = \frac{4}{3} \pi r^3 }$
• Calculator: Use a calculator to evaluate the expression and get the final answer.

Q: What is the significance of the constant $\frac{4}{3} \pi$ in the formula for the volume of a sphere?

A: The constant $\frac{4}{3} \pi$ is a fundamental constant in mathematics that is used to calculate the volume of a sphere. It is derived from the fact that the volume of a sphere is proportional to the cube of its radius.

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

A: No, the formula for the volume of a sphere is not the same as the formula for the volume of a cone. The formula for the volume of a cone is given by ${ V = \frac{1}{3} \pi r^2 h }$, where $r$ is the radius of the cone and $h$ is the height of the cone.

Conclusion

In this article, we answered some frequently asked questions about calculating the volume of a sphere. We covered topics such as the formula for the volume of a sphere, the relationship between the radius and the volume of a sphere, and how to calculate the volume of a sphere using a calculator. We also discussed the significance of the constant $\frac{4}{3} \pi$ in the formula for the volume of a sphere.

Related Topics

• Volume of a Cylinder: The volume of a cylinder is given by ${ V = \pi r^2 h }$, where $r$ is the radius of the cylinder and $h$ is the height of the cylinder.
• Surface Area of a Sphere: The surface area of a sphere is given by ${ A = 4 \pi r^2 }$, where $r$ is the radius of the sphere.
• Volume of a Cone: The volume of a cone is given by ${ V = \frac{1}{3} \pi r^2 h }$, where $r$ is the radius of the cone and $h$ is the height of the cone.

References

• Mathematics Handbook: A comprehensive handbook of mathematical formulas and theorems.
• Geometry and Trigonometry: A textbook on geometry and trigonometry that covers the basics of these subjects.
• Calculus: A textbook on calculus that covers the basics of this subject.

Further Reading

• Mathematics for Engineers: A textbook on mathematics for engineers that covers the basics of mathematics as applied to engineering.
• Mathematics for Scientists: A textbook on mathematics for scientists that covers the basics of mathematics as applied to science.
• Mathematics for Computer Scientists: A textbook on mathematics for computer scientists that covers the basics of mathematics as applied to computer science.