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Cylinder Surface Area Calculator

Introduction

Welcome to our Cylinder Surface Area Calculator!, which helps you calculate the lateral and total surface area of cylinder with ease. A cylinder is a solid three-dimensional geometric shape. It has two parallel circular bases at either end of the cylinder and a curved surface connecting them. Further, the perpendicular distance between the bases is the height of the cylinder. The cylinder’s dimensions also include the radius, which is the distance from the center of the base to the circumference of the cylinder.

The lateral surface area of the cylinder is the area of the curved part of the cylinder. Whereas, the total surface area of the cylinder is the sum of the area of the curved part of the cylinder and the area of the two circular bases.

How to use Cylinder Surface Area Calculator?

Using the Cylinder Surface Area Calculator, you can calculate the lateral surface area and the total surface of the cylinder by inputting the variables like the radius and also height of the cylinder.

The variables in the calculator include

Radius (r) The distance between the center of the base to the circumference of the base.

Height (h) The length of the perpendicular from one of the bases to the other base of the cylinder.

Lateral Surface Area (LSA) The area of the curved surface of the cylinder.

Total Surface Area (TSA) The sum of the curved surface area and the area of the two bases of the cylinder.

What is a Cylinder?

A cylinder is a solid three-dimensional shape with two circular bases at each end, joined by a curved surface. The height of the cylinder is the distance between the two bases. The radius of the cylinder is the distance between the center and the circumference of the base of the cylinder.

Types of Cylinders

There are four different types of cylinders.

  1. Right Circular Cylinder: In a right circular cylinder, the axis is perpendicular to the base, and so the axis passes through the center of the base.

  2. Oblique cylinder: In an oblique cylinder, the sides of the cylinder are not perpendicular to the base. So, both the bases of the cylinder are not directly aligned with each other. Hence the axis of the cylinder will be inclined at an angle with the base.

Properties of the Cylinder

  1. The cylinder will have two identical bases parallel to each other and one curved surface connecting the two bases.

  2. The cylinder’s dimensions include the base’s radius and also the curved surface’s height.

  3. The central axis of the cylinder is the line that passes through the centers of the two circular bases and is perpendicular to the bases.

How is the Lateral Surface Area of the Cylinder Calculated?

The lateral surface area of the cylinder is the area of the curved surface of the cylinder.

We can calculate the lateral surface area of the cylinder by using the following formula.

LSA=2πrh\text{LSA} = 2\pi r h

Where,

r = Radius of the base of the cylinder

h = Height of the cylinder

How is the Total Surface Area of the Cylinder Calculated?

The total surface area of the cylinder is the area of the curved surface of the cylinder plus the area of the two bases.

We can calculate the total surface area of the cylinder by using the following formula.

TSA=2πr(h+r)\text{TSA} = 2\pi r ( h + r)

Where,

r = Radius of the base of the cylinder

h = Height of the cylinder

Examples

Given a cylinder with radius of 5 cm and height of 10 cm. Calculate the lateral surface area and also the total surface area of the cylinder.

We can calculate the lateral surface area of the cylinder using the following formula

LSA=2πrh=2⋅π⋅5⋅10=314.16  cm2\begin{aligned} \text{LSA} &= 2 \pi r h \\[10pt] &= 2 \cdot \pi \cdot5\cdot10 \\[10pt] &= 314.16 \; cm^2 \end{aligned}

we can calculate the total surface area of the cylinder using the following formula

TSA=2πr(h+r)=2⋅π⋅5(10+5)=471.24  cm2\begin{aligned} \text{TSA} &= 2\pi r (h + r) \\[10pt] &= 2 \cdot \pi \cdot 5 (10 + 5) \\[10pt] &= 471.24 \; cm^2 \end{aligned}
Author

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Our team blends expertise in mathematics, finance, engineering, physics, and statistics to create advanced, user-friendly calculators. We ensure accuracy, robustness, and simplicity, catering to professionals, students, and enthusiasts. Our diverse skills make complex calculations accessible and reliable for all users.

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