Understanding the Given Dimensions

Oct 13, 2025 by sorusgentrification.com 114 views

Introduction

In mathematics, a right cylinder is a three-dimensional shape with two parallel and circular bases connected by a curved lateral surface. In this article, we will explore how to calculate the volume of a right cylinder using the given dimensions. We will use the formula for the volume of a cylinder, which is V = πr²h, where V is the volume, π is a mathematical constant approximately equal to 3.14, r is the radius of the base, and h is the height of the cylinder.

Understanding the Given Dimensions

Brianna has measured the height of the can as 6 1/4 inches and its radius as 3/4 inches. To make calculations easier, we can convert the mixed number 6 1/4 to an improper fraction. The mixed number 6 1/4 is equal to the improper fraction 25/4.

Converting the Mixed Number to an Improper Fraction

To convert the mixed number 6 1/4 to an improper fraction, we multiply the whole number part (6) by the denominator (4) and add the numerator (1). This gives us:

6 × 4 + 1 = 24 + 1 = 25

So, the mixed number 6 1/4 is equal to the improper fraction 25/4.

Calculating the Volume of the Cylinder

Now that we have the given dimensions, we can calculate the volume of the cylinder using the formula V = πr²h. We will substitute the values of r and h into the formula and calculate the volume.

Step 1: Substitute the Values of r and h

The radius of the base (r) is 3/4 inches, and the height of the cylinder (h) is 25/4 inches. We will substitute these values into the formula V = πr²h.

V = π(3/4)²(25/4)

Step 2: Calculate the Square of the Radius

To calculate the square of the radius, we will multiply the radius by itself.

(3/4)² = (3/4) × (3/4) = 9/16

Step 3: Substitute the Square of the Radius into the Formula

Now that we have calculated the square of the radius, we will substitute this value into the formula V = πr²h.

V = π(9/16)(25/4)

Step 4: Multiply the Numerators and Denominators

To multiply the numerators and denominators, we will multiply the numerators together and the denominators together.

9 × 25 = 225 16 × 4 = 64

Step 5: Simplify the Fraction

Now that we have multiplied the numerators and denominators, we will simplify the fraction.

V = π(225/64)

Step 6: Multiply by π

To calculate the volume, we will multiply the fraction by π.

V = (225/64) × π V ≈ (225/64) × 3.14 V ≈ 17.57

Conclusion

In this article, we have calculated the volume of a right cylinder using the given dimensions. We have used the formula V = πr²h and substituted the values of r and h into the formula. We have calculated the square of the radius, multiplied the numerators and denominators, simplified the fraction, and multiplied by π. The final answer is approximately 17.57 cubic inches.

Discussion

The calculation of the volume of a right cylinder is an important concept in mathematics. It is used in various fields such as engineering, architecture, and physics. The formula V = πr²h is a fundamental concept in mathematics, and it is used to calculate the volume of various shapes such as cylinders, cones, and spheres.

Real-World Applications

The calculation of the volume of a right cylinder has various real-world applications. For example, in engineering, it is used to calculate the volume of pipes, tubes, and other cylindrical shapes. In architecture, it is used to calculate the volume of buildings, bridges, and other structures. In physics, it is used to calculate the volume of objects such as balls, cylinders, and cones.

Conclusion

Introduction

In our previous article, we calculated the volume of a right cylinder using the formula V = πr²h. In this article, we will answer some frequently asked questions about calculating the volume of a right cylinder.

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

A: The formula for the volume of a right cylinder is V = πr²h, where V is the volume, π is a mathematical constant approximately equal to 3.14, r is the radius of the base, and h is the height of the cylinder.

Q: How do I calculate the square of the radius?

A: To calculate the square of the radius, you will multiply the radius by itself. For example, if the radius is 3/4 inches, you will calculate (3/4)² = (3/4) × (3/4) = 9/16.

Q: What if the radius is a mixed number? How do I convert it to an improper fraction?

A: To convert a mixed number to an improper fraction, you will multiply the whole number part by the denominator and add the numerator. For example, if the mixed number is 6 1/4, you will calculate 6 × 4 + 1 = 24 + 1 = 25. So, the mixed number 6 1/4 is equal to the improper fraction 25/4.

Q: How do I multiply the numerators and denominators?

A: To multiply the numerators and denominators, you will multiply the numerators together and the denominators together. For example, if you have the fraction 9/16 and you multiply it by 25/4, you will calculate 9 × 25 = 225 and 16 × 4 = 64.

Q: What if I have a decimal value for the radius or height? How do I calculate the volume?

A: If you have a decimal value for the radius or height, you can plug it into the formula V = πr²h and calculate the volume. For example, if the radius is 0.75 inches and the height is 6.25 inches, you will calculate V = π(0.75)²(6.25).

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

A: Yes, you can use a calculator to calculate the volume of a right cylinder. Simply plug in the values of r and h into the formula V = πr²h and calculate the volume.

Q: What are some real-world applications of calculating the volume of a right cylinder?

A: Calculating the volume of a right cylinder has various real-world applications. For example, in engineering, it is used to calculate the volume of pipes, tubes, and other cylindrical shapes. In architecture, it is used to calculate the volume of buildings, bridges, and other structures. In physics, it is used to calculate the volume of objects such as balls, cylinders, and cones.

Conclusion

In conclusion, calculating the volume of a right cylinder is an important concept in mathematics. The formula V = πr²h is a fundamental concept in mathematics, and it is used to calculate the volume of various shapes such as cylinders, cones, and spheres. We hope that this Q&A article has helped to clarify any questions you may have had about calculating the volume of a right cylinder.

Additional Resources

If you are interested in learning more about calculating the volume of a right cylinder, we recommend checking out the following resources:

Khan Academy: Calculating the Volume of a Cylinder
Mathway: Calculating the Volume of a Cylinder
Wolfram Alpha: Calculating the Volume of a Cylinder

We hope that this article has been helpful in answering your questions about calculating the volume of a right cylinder. If you have any further questions, please don't hesitate to contact us.