How to Calculate the Surface Area of a Cylinder

Cylinder with Radius r and Height h

Basic geometry defines a cylinder as a surface formed by the points that are a fixed distance from a given line segment called the axis of the cylinder. The resulting solid that is formed by the intersection of this surface with two planes perpendicular to the axis of the cylinder may also be called a cylinder. The surface area of cylinder is the total surface area of all of its faces. You can calculate the surface area of a cylinder if you know its radius and height.

Things You'll Need

• Calculator

Instructions

1. Identify the three individual surfaces of a cylinder. These include two circles, each one is at an end of the cylinder. The third surface is formed by "wrapping" a rectangle around the circles.

2. Determine the area of the two circles of the cylinder. The area of a circle is equal to (pi)(r^2) where r is the radius of the cylinder.

3. Calculate the rectangular area of the cylinder. Note that this area is equal to that of a rectangle of height h times length c, where h is the height of the cylinder and c is the circumference of the cylinder. Since c = 2(pi)r by the definition of pi, the area of this rectangle is therefore hc = h2(pi)r.

4. Calculate the area of the cylinder using the surface areas found in Steps 2 and 3. The area A of the cylinder is given by A = (pi)(r^2) + (pi)(r^2) + h2(pi)r.

5. Simplify the equation for the area given in Step 4. A = (pi)(r^2) + (pi)(r^2) + h2(pi)r = (pi)(r^2 + r^2 + 2rh) = (pi)(2r^2 + 2rh) = 2r(pi)(r + h).

References

• Math.com