Calculating the Surface Area of a Cylinder with Specific Dimensions

The surface area of a cylinder is an important geometric measurement that helps us understand the properties of three-dimensional shapes. When given specific dimensions, such as the height and radius, we can easily calculate the surface area using the appropriate formula. This article will guide you through the process of calculating the surface area of a cylinder with a height of 5 meters and a radius of 150 centimeters (which is 1.5 meters). We'll also explore the significance of this measurement and its practical applications.

Understanding the Formula

The formula for calculating the surface area of a cylinder is given by:

![Surface Area Formula]()

The surface area (A) of a cylinder can be found using the formula:

A 2πr 2 2πrh

Where:

r is the radius of the cylinder's base. h is the height of the cylinder. π (pi) is a mathematical constant approximately equal to 3.14159.

Solving the Problem

Let's apply this formula to the given dimensions. The height of the cylinder is 5 meters, and the radius is 150 centimeters, which is converted to 1.5 meters.

Conversion and Calculation

In order to use the formula, we need to convert the radius into meters:

Radius (r) 150 cm 1.5 m

The height (h) of the cylinder is already given in meters:

Height (h) 5 m

Step-by-Step Calculation

Now, we can substitute the values into the formula:

Surface Area (A) 2πr2 2πrh

Substituting the values r 1.5 m and h 5 m:

A 2π(1.5)2 2π(1.5)(5)

A 2π(2.25) 2π(7.5)

A 4.5π 15π

A 19.5π

Using Pi (π)

Since π is approximately 3.14159, we can further simplify this:

A ≈ 19.5 x 3.14159

A ≈ 61.065 m2

However, if we take the more accurate value of π as 22/7, we get:

A 19.5 x (22/7)

A 61.72857143 m2

Final Result

The surface area of the cylinder is approximately 61.72857143 square meters, or rounded to two decimal places, 61.73 square meters.

Practical Applications of Surface Area Calculation

The calculation of the surface area of a cylinder has numerous practical applications in various fields, including:

Engineering and Construction

In engineering projects, accurate surface area calculations are crucial for determining the amount of material needed, such as paint, wallpaper, or roofing material. This not only ensures cost effectiveness but also minimizes waste.

Manufacture and Packaging

In the field of packaging design, the surface area of a cylinder is essential for creating appropriate containers. It helps in determining the size and quantity of material required for the packaging, leading to optimized designs and cost savings.

Environmental Science

Understanding the surface area can be vital in environmental studies, particularly in assessing the exposure of cylindrical structures to external factors such as wind, precipitation, and temperature changes.

Conclusion

Calculating the surface area of a cylinder is a fundamental skill in geometry that has practical applications across various industries. By mastering this calculation, you can solve real-world problems more effectively and efficiently.

Additional Resources

For those interested in learning more about surface area and other geometric calculations, consider exploring:

Online tutorials and interactive calculators

Books on geometry and engineering

Video tutorials on YouTube and other educational platforms

By delving deeper into these resources, you can enhance your understanding and proficiency in this critical area of mathematics.