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The total area of a figure is the sum of the areas of all its faces. To find the area of the cylinder, you need to find the area of the two bases and add the area of the surrounding face. The formula for the area of a cylinder is A = 2πr 2 + 2πrh.
Steps
Calculate the area of 2 circles (2 x (π xr 2 ))
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Visualize the two bases of the cylinder. Imagine the shape of the soup box as it is cylindrical. You will see that its top and bottom faces are the same. Both are circular. The first step to finding the total area of the cylinder is to find the areas of these two circles. [1] X Research Source
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Find the radius of the cylinder. The radius is the distance from the center of the circle to a point on the circle, denoted by the letter “r.” The radius of the cylinder is also equal to the radius of the base circle. In this example, the radius of the base circle is 3 cm. [2] X Research Source
- If it is a puzzle problem, the radius can be a given fact. The problem can also give diameter data, i.e. the distance from one side point to the other on the circle and passing through the center of the circle. The radius is half the length of the diameter.
- You can use a radius ruler if you are calculating the total area of a truly cylindrical object.
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Calculate the area of the circle above. The area of a circle is equal to pi (~3.14) times the square of its radius. The equation is written as π xr 2 , otherwise as π xrx r.
- To find the area of the base, simply substitute the radius 3 cm into the equation to find the area of the circle: A = πr 2 . Here’s how to do it: [3] X Research Source
- A = r 2
- A = x 3 2
- A = x 9 = 28.26 cm 2
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Do the same for the circle at the other end. Once you’ve found the area of one bottom, you’ll have to add up the area of the second bottom as well. You can do the same steps as you did with the first bottom, or you find that the two bottoms are the same. You probably don’t need to use the equation for the area of a circle for the second base if you understand this. [4] X Research Sources
Calculate the area of the surrounding face (2π xrxh)
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Visualize the circumference of the cylinder. When you imagine the shape of the soup box, you will see that it has a top bottom and a bottom bottom. These two bottoms are connected by the “wall” of the box. The radius of the wall of the box is also the radius of the bottom, but unlike the bottom, the surrounding wall also has a height. [5] X Research Sources
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Find the circumference of the circle. You will need to find the perimeter to find the area of the surrounding face. To find the circumference of a circle, you simply multiply the radius by 2π. Thus, the circumference can be calculated by multiplying 3 cm by 2π. 3 cm x 2π = 18.84 cm. [6] X Research Source
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Multiply the circumference of the circle by the height of the cylinder. This calculation will give the area of the surrounding face. Multiply the circumference (= 18.84 cm) by the height (5 cm). 18.84 cm x 5 cm = 94.2 cm 2 . [7] X Research Sources
Add the two results together ((2) x ( π xr 2 )) + (2π xrxh)
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Visualize the entire cylinder. First, you will imagine the two bases of the cylinder and calculate their total area. Next, think about the circumference connecting the two bases of the cylinder and calculate the area. This time, think about the entire cylinder and calculate the area of its entire surface. [8] X Research Sources
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Double the area of a base. You simply multiply the result 28.26 cm 2 by 2 to get the area of the 2 bases. 28.26 x 2 = 56.52 cm 2 . So you have the sum of the areas of the 2 bases.
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Add the area of the surrounding face to the area of the base. After adding the areas of the two bases with the area of the surrounding faces, you will find the total area of the cylinder. All you need to do is add the area of the two bases (56.52 cm 2 ) with the area around (94.2 cm 2 ). 56.52 cm 2 + 94.2 cm 2 = 150.72 cm 2 . The total area of a cylinder with a height of 5 cm and a base of a circle with a radius of 3 cm is 150.72 cm 2 . [9] X Research Source
Advice
- If the height or radius includes a square root, refer to How to multiply square roots and How to add and subtract square roots for more information.
Warning
- Always remember to double the area of the base to include the second base in the calculation.
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This article is co-authored by a team of editors and trained researchers who confirm the accuracy and completeness of the article.
The wikiHow Content Management team carefully monitors the work of editors to ensure that every article is up to a high standard of quality.
This article has been viewed 37,262 times.
The total area of a figure is the sum of the areas of all its faces. To find the area of the cylinder, you need to find the area of the two bases and add the area of the surrounding face. The formula for the area of a cylinder is A = 2πr 2 + 2πrh.
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