Find The Volume Of A Cylinder With Radius 26 Cm And Height 21 Cm.The Volume \[$ V \$\] Of A Cylinder Is Given By The Formula:$\[ V = \pi R^2 H \\]Use 3.14 For \[$\pi\$\] Or The \[$\pi\$\] Key On Your Calculator. Round

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 $V = \pi r^2 h$, where $r$ is the radius of the cylinder and $h$ is its height. In this article, we will use the formula to find the volume of a cylinder with a radius of 26 cm and a height of 21 cm.

Understanding the Formula

The formula for the volume of a cylinder is $V = \pi r^2 h$. This formula can be broken down into three main components:

• Radius ($r$): The radius of the cylinder is the distance from the center of the cylinder to the edge. In this case, the radius is 26 cm.
• Height ($h$): The height of the cylinder is the distance from the top to the bottom of the cylinder. In this case, the height is 21 cm.
• Pi ($\pi$): Pi is a mathematical constant that is approximately equal to 3.14. It is used to calculate the volume of the cylinder.

Calculating the Volume

To calculate the volume of the cylinder, we need to plug in the values of the radius, height, and pi into the formula. We will use the value of pi as 3.14.

Step 1: Square the Radius

The first step is to square the radius of the cylinder. This means multiplying the radius by itself.

$r^2 = 26^2 = 676$

Step 2: Multiply the Squared Radius by the Height

The next step is to multiply the squared radius by the height of the cylinder.

$676 \times 21 = 14216$

Step 3: Multiply by Pi

The final step is to multiply the result by pi.

$14216 \times 3.14 = 44651.84$

Rounding the Answer

The final answer should be rounded to the nearest whole number. In this case, the volume of the cylinder is approximately 44652 cubic centimeters.

Conclusion

In this article, we used the formula for the volume of a cylinder to find the volume of a cylinder with a radius of 26 cm and a height of 21 cm. We broke down the formula into three main components and calculated the volume step by step. The final answer was approximately 44652 cubic centimeters.

Real-World Applications

The formula for the volume of a cylinder has many real-world applications. For example:

• Architecture: Architects use the formula to calculate the volume of buildings and other structures.
• Engineering: Engineers use the formula to calculate the volume of pipes and other cylindrical objects.
• Science: Scientists use the formula to calculate the volume of cells and other biological structures.

Common Mistakes

When calculating the volume of a cylinder, there are several common mistakes to avoid:

• Rounding errors: Rounding errors can occur when calculating the squared radius or multiplying the result by pi.
• Incorrect values: Incorrect values for the radius, height, or pi can lead to incorrect results.
• Lack of precision: Lack of precision can lead to incorrect results, especially when working with large numbers.

Tips and Tricks

Here are some tips and tricks to help you calculate the volume of a cylinder:

• Use a calculator: Using a calculator can help you avoid rounding errors and calculate the volume quickly and accurately.
• Check your values: Double-check your values for the radius, height, and pi to ensure that they are correct.
• Use a formula sheet: Keep a formula sheet handy to help you remember the formula for the volume of a cylinder.

Conclusion

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

A: The formula for the volume of a cylinder is $V = \pi r^2 h$, where $r$ is the radius of the cylinder and $h$ is its height.

Q: What is the value of pi ($\pi$) used in the formula?

A: The value of pi ($\pi$) used in the formula is approximately 3.14.

Q: How do I calculate the volume of a cylinder with a radius of 25 cm and a height of 20 cm?

A: To calculate the volume of a cylinder with a radius of 25 cm and a height of 20 cm, you can use the formula $V = \pi r^2 h$. Plugging in the values, you get:

$V = \pi (25)^2 (20)$ $V = 3.14 (625) (20)$ $V = 3.14 (12500)$ $V = 39250$

Q: What is the volume of a cylinder with a radius of 30 cm and a height of 15 cm?

A: To calculate the volume of a cylinder with a radius of 30 cm and a height of 15 cm, you can use the formula $V = \pi r^2 h$. Plugging in the values, you get:

$V = \pi (30)^2 (15)$ $V = 3.14 (900) (15)$ $V = 3.14 (13500)$ $V = 42330$

Q: How do I calculate the volume of a cylinder with a radius of 20 cm and a height of 10 cm?

A: To calculate the volume of a cylinder with a radius of 20 cm and a height of 10 cm, you can use the formula $V = \pi r^2 h$. Plugging in the values, you get:

$V = \pi (20)^2 (10)$ $V = 3.14 (400) (10)$ $V = 3.14 (4000)$ $V = 12560$

Q: What is the volume of a cylinder with a radius of 40 cm and a height of 25 cm?

A: To calculate the volume of a cylinder with a radius of 40 cm and a height of 25 cm, you can use the formula $V = \pi r^2 h$. Plugging in the values, you get:

$V = \pi (40)^2 (25)$ $V = 3.14 (1600) (25)$ $V = 3.14 (40000)$ $V = 125600$

Q: How do I calculate the volume of a cylinder with a radius of 15 cm and a height of 5 cm?

A: To calculate the volume of a cylinder with a radius of 15 cm and a height of 5 cm, you can use the formula $V = \pi r^2 h$. Plugging in the values, you get:

$V = \pi (15)^2 (5)$ $V = 3.14 (225) (5)$ $V = 3.14 (1125)$ $V = 3531.5$

Q: What is the volume of a cylinder with a radius of 50 cm and a height of 30 cm?

A: To calculate the volume of a cylinder with a radius of 50 cm and a height of 30 cm, you can use the formula $V = \pi r^2 h$. Plugging in the values, you get:

$V = \pi (50)^2 (30)$ $V = 3.14 (2500) (30)$ $V = 3.14 (75000)$ $V = 235500$

Conclusion

In conclusion, the formula for the volume of a cylinder is a fundamental concept in mathematics that has many real-world applications. By following the steps outlined in this article, you can calculate the volume of a cylinder with ease. Remember to use a calculator to ensure accuracy and to check your values to ensure that they are correct.