The Volume Of A Cylinder Measuring 5 Inches In Diameter And 6 Inches Tall Is:A. 471 Cubic Inches B. 94.2 Cubic Inches C. 117.75 Cubic Inches
Introduction
In mathematics, the volume of a cylinder is a fundamental concept that is used to calculate the amount of space inside a cylindrical object. The formula for the volume of a cylinder is given by V = πr²h, where V is the volume, π is a mathematical constant approximately equal to 3.14, r is the radius of the base of the cylinder, and h is the height of the cylinder. In this article, we will use this formula to calculate the volume of a cylinder with a diameter of 5 inches and a height of 6 inches.
Understanding the Formula
The formula for the volume of a cylinder is V = πr²h. To use this formula, we need to know the values of r and h. The radius of the base of the cylinder is half of the diameter, so if the diameter is 5 inches, the radius is 2.5 inches. The height of the cylinder is given as 6 inches.
Calculating the Volume
Now that we have the values of r and h, we can plug them into the formula to calculate the volume of the cylinder. The formula becomes V = π(2.5)²(6). To calculate this, we need to follow the order of operations (PEMDAS):
- Calculate the square of the radius: (2.5)² = 6.25
- Multiply the result by π: 6.25 × 3.14 = 19.625
- Multiply the result by the height: 19.625 × 6 = 117.75
Therefore, the volume of the cylinder is 117.75 cubic inches.
Comparing the Answer
Now that we have calculated the volume of the cylinder, we can compare our answer to the options given in the problem. The options are:
A. 471 cubic inches B. 94.2 cubic inches C. 117.75 cubic inches
Our calculated answer is 117.75 cubic inches, which matches option C.
Conclusion
In this article, we used the formula for the volume of a cylinder to calculate the volume of a cylinder with a diameter of 5 inches and a height of 6 inches. We followed the order of operations to calculate the volume and found that it is 117.75 cubic inches. This answer matches option C, which is the correct answer.
Real-World Applications
The formula for the volume of a cylinder has many real-world applications. For example, it can be used to calculate the volume of a water tank, a pipe, or a container. It can also be used to calculate the volume of a cylindrical object, such as a can or a bottle.
Tips and Tricks
Here are some tips and tricks to help you remember the formula for the volume of a cylinder:
- The formula is V = πr²h, where V is the volume, π is a mathematical constant, r is the radius of the base of the cylinder, and h is the height of the cylinder.
- The radius of the base of the cylinder is half of the diameter.
- To calculate the volume, follow the order of operations (PEMDAS).
- Practice, practice, practice! The more you practice, the more comfortable you will become with the formula and the calculations.
Common Mistakes
Here are some common mistakes to avoid when calculating the volume of a cylinder:
- Forgetting to square the radius.
- Forgetting to multiply the result by π.
- Forgetting to multiply the result by the height.
- Not following the order of operations (PEMDAS).
Conclusion
Introduction
In our previous article, we discussed the formula for the volume of a cylinder and used it to calculate the volume of a cylinder with a diameter of 5 inches and a height of 6 inches. In this article, we will answer some frequently asked questions about the volume of a cylinder.
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, π is a mathematical constant approximately equal to 3.14, r is the radius of the base of the cylinder, and h is the height of the cylinder.
Q: How do I calculate the volume of a cylinder?
A: To calculate the volume of a cylinder, you need to follow the order of operations (PEMDAS):
- Calculate the square of the radius: (r)²
- Multiply the result by π: (r)² × π
- Multiply the result by the height: (r)² × π × h
Q: What is the radius of the base of a cylinder?
A: The radius of the base of a cylinder is half of the diameter. If the diameter is 5 inches, the radius is 2.5 inches.
Q: How do I calculate the volume of a cylinder with a diameter of 10 inches and a height of 8 inches?
A: To calculate the volume of a cylinder with a diameter of 10 inches and a height of 8 inches, you need to follow the order of operations (PEMDAS):
- Calculate the square of the radius: (5)² = 25
- Multiply the result by π: 25 × 3.14 = 78.5
- Multiply the result by the height: 78.5 × 8 = 627.2
Therefore, the volume of the cylinder is 627.2 cubic inches.
Q: What is the volume of a cylinder with a radius of 3 inches and a height of 9 inches?
A: To calculate the volume of a cylinder with a radius of 3 inches and a height of 9 inches, you need to follow the order of operations (PEMDAS):
- Calculate the square of the radius: (3)² = 9
- Multiply the result by π: 9 × 3.14 = 28.26
- Multiply the result by the height: 28.26 × 9 = 254.34
Therefore, the volume of the cylinder is 254.34 cubic inches.
Q: How do I convert the volume of a cylinder from cubic inches to cubic feet?
A: To convert the volume of a cylinder from cubic inches to cubic feet, you need to divide the volume in cubic inches by 1,728 (since there are 1,728 cubic inches in a cubic foot).
Q: What are some real-world applications of the formula for the volume of a cylinder?
A: The formula for the volume of a cylinder has many real-world applications, such as:
- Calculating the volume of a water tank
- Calculating the volume of a pipe
- Calculating the volume of a container
- Calculating the volume of a cylindrical object, such as a can or a bottle
Conclusion
In conclusion, the formula for the volume of a cylinder is V = πr²h, and it has many real-world applications. By following the order of operations and practicing, you can become more comfortable with the formula and the calculations. We hope this Q&A guide has been helpful in answering your questions about the volume of a cylinder.