Volume of a Cylinder Formula

Oct 13, 2025 by thesweetdesigns.com 77 views

Introduction

In this article, we will explore the concept of calculating the height of a cylindrical sandbox given its radius and the volume of sand it can hold. We will use mathematical formulas to determine the height of the sandbox, making it a fun and interactive problem for math enthusiasts.

Understanding the Problem

Tina is making a cylindrical sandbox with a radius of 2 feet. She has bought 18.84 cubic feet of sand for the sandbox. The problem is to find the height of the sandbox that will fit all the sand. To solve this problem, we need to use the formula for the volume of a cylinder, which is given by:

Volume of a Cylinder Formula

The formula for the volume of a cylinder is:

V = πr²h

Where:

V is the volume of the cylinder
π (pi) is a mathematical constant approximately equal to 3.14
r is the radius of the cylinder
h is the height of the cylinder

Given Values

We are given the following values:

Radius (r) = 2 feet
Volume (V) = 18.84 cubic feet

Solving for Height

We can now substitute the given values into the formula for the volume of a cylinder:

18.84 = π(2)²h

To solve for h, we need to isolate h on one side of the equation. We can do this by dividing both sides of the equation by π(2)²:

h = 18.84 / (π(2)²)

Calculating the Height

Now, we can calculate the height of the sandbox by plugging in the value of π (approximately 3.14) and solving for h:

h = 18.84 / (3.14(2)²) h = 18.84 / (3.14(4)) h = 18.84 / 12.56 h = 1.5

Conclusion

Therefore, Tina needs to make the sandbox with a height of 1.5 feet to fit all the sand.

Discussion

This problem is a great example of how math can be used in real-world applications. By using the formula for the volume of a cylinder, we can calculate the height of the sandbox that will fit all the sand. This problem also requires the use of mathematical constants, such as π, and the ability to solve equations.

Answer

The correct answer is:

D. 1.5 ft

Mathematical Formulas

Volume of a cylinder: V = πr²h
Circumference of a circle: C = 2πr
Area of a circle: A = πr²

Mathematical Constants

π (pi): approximately 3.14
e (Euler's number): approximately 2.718
√2 (square root of 2): approximately 1.414

Mathematical Operations

Addition: a + b
Subtraction: a - b
Multiplication: a × b
Division: a ÷ b

Mathematical Functions

Exponential function: f(x) = ax
Logarithmic function: f(x) = log(x)
Trigonometric functions: sin(x), cos(x), tan(x)
Q&A: Calculating the Height of a Cylindrical Sandbox =====================================================

Introduction

In our previous article, we explored the concept of calculating the height of a cylindrical sandbox given its radius and the volume of sand it can hold. We used mathematical formulas to determine the height of the sandbox, making it a fun and interactive problem for math enthusiasts. In this article, we will answer some frequently asked questions related to this topic.

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

A: The formula for the volume of a cylinder is:

V = πr²h

Where:

V is the volume of the cylinder
π (pi) is a mathematical constant approximately equal to 3.14
r is the radius of the cylinder
h is the height of the cylinder

Q: How do I calculate the height of a cylinder given its radius and volume?

A: To calculate the height of a cylinder, you can use the formula:

h = V / (πr²)

Where:

V is the volume of the cylinder
π (pi) is a mathematical constant approximately equal to 3.14
r is the radius of the cylinder

Q: What if I don't know the value of π? Can I still calculate the height of the cylinder?

A: Yes, you can still calculate the height of the cylinder even if you don't know the value of π. You can use an approximate value of π, such as 3.14, or you can use a calculator to find the value of π.

Q: How do I calculate the volume of a cylinder given its radius and height?

A: To calculate the volume of a cylinder, you can use the formula:

V = πr²h

Where:

V is the volume of the cylinder
π (pi) is a mathematical constant approximately equal to 3.14
r is the radius of the cylinder
h is the height of the cylinder

Q: What if I have a cylinder with a radius of 2 feet and a height of 4 feet? What is its volume?

A: To find the volume of the cylinder, you can use the formula:

V = πr²h

Substituting the values, we get:

V = π(2)²(4) V = 3.14(4)(4) V = 50.24

Therefore, the volume of the cylinder is approximately 50.24 cubic feet.

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

A: No, this formula is only for calculating the volume of a cylinder. If you want to calculate the volume of a sphere, you will need to use a different formula.

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

A: The formula for the volume of a sphere is:

V = (4/3)πr³

Where:

V is the volume of the sphere
π (pi) is a mathematical constant approximately equal to 3.14
r is the radius of the sphere

Q: How do I calculate the radius of a cylinder given its volume and height?

A: To calculate the radius of a cylinder, you can use the formula:

r = √(V / (πh))

Where:

V is the volume of the cylinder
π (pi) is a mathematical constant approximately equal to 3.14
h is the height of the cylinder

Q: Can I use this formula to calculate the radius of a sphere?

A: No, this formula is only for calculating the radius of a cylinder. If you want to calculate the radius of a sphere, you will need to use a different formula.

Conclusion

In this article, we have answered some frequently asked questions related to calculating the height of a cylindrical sandbox. We have also provided formulas for calculating the volume and radius of a cylinder and a sphere. We hope this article has been helpful in understanding these concepts.

Calculating the Height of a Cylindrical Sandbox
Understanding the Formula for the Volume of a Cylinder
Calculating the Volume of a Sphere

Mathematical Formulas

Volume of a cylinder: V = πr²h
Circumference of a circle: C = 2πr
Area of a circle: A = πr²
Volume of a sphere: V = (4/3)πr³

Mathematical Constants

π (pi): approximately 3.14
e (Euler's number): approximately 2.718
√2 (square root of 2): approximately 1.414

Mathematical Operations

Addition: a + b
Subtraction: a - b
Multiplication: a × b
Division: a ÷ b

Mathematical Functions

Exponential function: f(x) = ax
Logarithmic function: f(x) = log(x)
Trigonometric functions: sin(x), cos(x), tan(x)