A Cylinder Has A Radius Of 14 M And A Height Of 6 M. What Is The Exact Volume Of The Cylinder?A. $84 \pi \, \text{m}^3$B. $168 \pi \, \text{m}^3$C. \$504 \pi \, \text{m}^3$[/tex\]D. $1176 \pi \, \text{m}^3$
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 = πr^2h, 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 exact volume of a cylinder with a radius of 14 m and a height of 6 m.
Understanding the Formula
The formula for the volume of a cylinder is V = πr^2h. This formula can be broken down into three main components:
- π (Pi): This is a mathematical constant that is approximately equal to 3.14. It is an irrational number that is used to represent the ratio of a circle's circumference to its diameter.
- r (Radius): This is the distance from the center of the base of the cylinder to the edge of the base. In this case, the radius is given as 14 m.
- h (Height): This is the distance from the base of the cylinder to the top of the cylinder. In this case, the height is given as 6 m.
Calculating the Volume
Now that we have a clear understanding of the formula, let's calculate the volume of the cylinder. We will use the given values of r = 14 m and h = 6 m.
V = πr^2h V = π(14)^2(6) V = π(196)(6) V = π(1176)
Simplifying the Expression
To simplify the expression, we can multiply the numbers together and then multiply the result by π.
V = π(1176) V = 3.14(1176) V = 3686.24
However, we are not done yet. We need to express the answer in terms of π, not as a decimal approximation.
V = π(1176) V = 1176π
Conclusion
In conclusion, the exact volume of the cylinder with a radius of 14 m and a height of 6 m is 1176Ï€ m^3. This is the correct answer, and it is the only one that matches the formula for the volume of a cylinder.
Comparison of Options
Let's compare our answer to the options given:
- A. 84Ï€ m^3: This is not the correct answer, as it is too small.
- B. 168Ï€ m^3: This is not the correct answer, as it is too small.
- C. 504Ï€ m^3: This is not the correct answer, as it is too small.
- D. 1176Ï€ m^3: This is the correct answer.
Final Answer
Introduction
In our previous article, we calculated the exact volume of a cylinder with a radius of 14 m and a height of 6 m. In this article, we will answer some frequently asked questions related to the calculation of 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 = πr^2h, 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: What is the significance of π in the formula?
A: π is a mathematical constant that is approximately equal to 3.14. It is an irrational number that is used to represent the ratio of a circle's circumference to its diameter. In the formula for the volume of a cylinder, π is used to calculate the area of the circular base.
Q: How do I calculate the volume of a cylinder with a given radius and height?
A: To calculate the volume of a cylinder with a given radius and height, you can use the formula V = πr^2h. Simply plug in the values of r and h into the formula and multiply them together.
Q: What if I want to express the answer in terms of π, rather than as a decimal approximation?
A: If you want to express the answer in terms of π, rather than as a decimal approximation, you can leave the answer as π multiplied by the result of the calculation. For example, if the calculation results in 1176, you can express the answer as 1176π.
Q: Can I use a calculator to calculate the volume of a cylinder?
A: Yes, you can use a calculator to calculate the volume of a cylinder. Simply enter the values of r and h into the calculator and multiply them together, then multiply the result by π.
Q: What if I want to calculate the volume of a cylinder with a non-integer radius or height?
A: If you want to calculate the volume of a cylinder with a non-integer radius or height, you can use the formula V = πr^2h and plug in the values of r and h. The result will be a decimal approximation of the volume.
Q: Can I use the formula for the volume of a cylinder to calculate the volume of a sphere?
A: No, you cannot use the formula for the volume of a cylinder to calculate the volume of a sphere. The formula for the volume of a sphere is V = (4/3)Ï€r^3, where V is the volume and r is the radius of the sphere.
Conclusion
In conclusion, the formula for the volume of a cylinder is V = πr^2h, 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. We hope that this article has answered some of your frequently asked questions related to the calculation of the volume of a cylinder.
Frequently Asked Questions
- Q: What is the formula for the volume of a cylinder? A: The formula for the volume of a cylinder is V = πr^2h.
- Q: What is the significance of π in the formula? A: π is a mathematical constant that is approximately equal to 3.14.
- Q: How do I calculate the volume of a cylinder with a given radius and height? A: To calculate the volume of a cylinder with a given radius and height, you can use the formula V = πr^2h.
- Q: Can I use a calculator to calculate the volume of a cylinder? A: Yes, you can use a calculator to calculate the volume of a cylinder.
Final Answer
The final answer is D. 1176Ï€ m^3.