How To Find The Total Surface Area Of A Closed Cylinder

Obtaining the area of a simple two-dimensional shape like a circle or rectangle requires following a simple formula, but determining the total surface area of a three-dimensional object like a cone or closed cylinder requires the use of multiple formulas. A cylinder's surface area is composed of two circular bases and a rectangle. The latter represents the cylinder's lateral surface. Calculating the total surface area requires calculating the sum of the base and lateral surface areas.

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Step 1

Calculate the base areas by using the formula for a circle's area: A = pi r^2. If the radius of the cylinder is 5, for instance, the area of one base is pi 5^2 or 25pi, while the area of both of the bases combined is 2 * 25pi, or 50pi.

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Step 2

Multiply the circumference of the base by the cylinder's height to determine the lateral area's surface area. If you were to tear the cylinder open and lay it flat on a table, you would discover the lateral area is simply a rectangle whose length is the base's circumference and whose width is the cylinder's height. Given a radius of 5, the circumference is 2 pi 5, or 10pi. Given a height of 10, multiply 10pi by 5 to obtain a lateral surface area of 50pi.

Step 3

Add the base areas to the lateral surface area to find the total surface area. Given the example, add 50pi to 50pi to obtain a total area of 100pi.

Cite This Article

MLA

Saxena, Vivek. "How To Find The Total Surface Area Of A Closed Cylinder" sciencing.com, https://www.sciencing.com/total-surface-area-closed-cylinder-12018531/. 24 April 2017.

APA

Saxena, Vivek. (2017, April 24). How To Find The Total Surface Area Of A Closed Cylinder. sciencing.com. Retrieved from https://www.sciencing.com/total-surface-area-closed-cylinder-12018531/

Chicago

Saxena, Vivek. How To Find The Total Surface Area Of A Closed Cylinder last modified March 24, 2022. https://www.sciencing.com/total-surface-area-closed-cylinder-12018531/

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