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How to Find the Surface Area of a Right Cylinder

A right cylinder is a cylinder in which the axis is perpendicular to the bases. Both ends are cut square and the cylinder stands vertically when rested on a horizontal surface. To understand how to determine the surface area, imagine a cylinder as a rectangle rolled into a tube. It has two dimensions: its height and its width. In the case of a cylinder, the width is wrapped around the tube and is called the circumference.

Things You'll Need

Tape measure

Instructions

- 1
  Measure the height of the cylinder. Measure at 90 degrees to the top edge, along a perfectly vertical line down the cylinder wall. Record the value. For this example, the height is 10 inches, so record "10."
- 2
  Measure the circumference of the cylinder along a line parallel to the top or bottom edge. Record the value. For this example, the circumference is 31 inches.
- 3
  Multiply the height by the circumference. The result is the surface area of an open-ended right cylinder. For the example, a height of 10 inches and a circumference of 31 inches means that the surface area is 310 square inches -- 10 times 31 equals 310.
- 4
  Determine the surface area of the base of a solid right cylinder by first dividing the circumference by pi, normally given as 3.1415. The result is the diameter of the cylinder. Divide the diameter by two to obtain the radius.
  In the example, if the circumference is 31 inches, then the radius is 4.934 inches -- 31 divided by 3.1415 equals 9.8679, and half of 9.8679 is 4.934.
- 5
  Square the radius and multiply the value by pi. The result is the surface area of the circle representing each base of the cylinder.
  For the example, if the radius if 4.934 inches then the surface area is 76.478 square inches -- 4.934 times 4.934 times 3.1415 equals 76.478.
- 6
  Multiply the area of the base by two to obtain the combined area of both ends, and then add the value to the surface area of the side walls. The result is the total surface area of a solid right cylinder.
  To conclude with the example, if the base area is 78.478 square inches, then both bases have a total area of 2 times 78.478 square inches, or 156.956 square inches. Add the surface area of the wall, 310 square inches, and the total area is 466.956 square inches.

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