How to Find the Area of Cylindrical Pipe Not Knowing the Height

From the toilet paper roll to the barrel of your pen, cylinders are part of your world. The surface of a perfect cylinder consists of 3 basic geometric shapes. The top and bottom of a cylinder are circles, while the curved side of the cylinder unwraps into a rectangle. You can calculate the surface area of the cylinder using the dimensions of the rectangle or the cylinder height, but a more innovative approach involves the cylinder capacity. Measure the volume of the cylinder and you can calculate how much area you need to encapsulate that volume.

Things You'll Need

  • Paper
  • Tape
  • Sand
  • Measuring cup
  • Ruler
  • Calculator
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Instructions

    • 1

      Measure the volume of the open-ended cylinder. Tape a piece of paper over one end of the cylinder to form a temporary seal. Fill the measuring cup with sand. Level the sand in the cup with a ruler. Scoop the sand into the cylinder. Repeat, until the cylinder is filled with sand. Count the number of cups of sand you transferred to the cylinder and multiply this by 236.6 to obtain the total volume of the cylinder in cm^3. Note that one measuring cup is equivalent to 236.6 ml or 236.6 cm^3. For example, a cylinder that accommodates 3 cups of sand has a volume of 709.8 cm^3 = (3 cups) x (236.6 cm^3/cup).

    • 2

      Measure the diameter of the cylinder using a ruler. The diameter is the maximum distance measured across the open end of the cylinder. Divide the diameter by 2 to obtain the radius (r) of the cylinder. The radius is the perpendicular distance from the long axis of symmetry of the cylinder to the curved wall of the cylinder. If the radius is measured in inches, convert the inches to centimeters using the relationship 1 inch = 2.54 cm. For example, a radius of 2 inches = 5.08 cm = 2 inch x 2.54 cm/inch.

    • 3

      Find the surface area of the open-ended cylinder by doubling the volume and dividing by the radius. For example, an open-ended cylindrical drain pipe having a radius of 5.08 cm and a volume of 709.8 cm^3 has a surface area of 279.4 cm^2 = (2 x 709.8 cm^3)/(5.08 cm) = (2 x volume)/(radius). For cylinders closed at one end, add [3.14 x (cylinder radius)^2] to the side surface area. For example, a cylindrical drinking glass has a volume of 236.6 cm^3 and a radius of 3 cm. The surface total surface area of this drinking glass is 186.0 cm^2 = [157.7 cm^2] + [28.3 cm^2] = [(2 x 236.6 cm^3)/(3 cm)] + [3.14 x (3 cm)^2] = [(2 x volume)/(radius)] + [3.14 x (cylinder radius)^2]. For cylinders closed at both ends, add 6.28 x (cylinder radius)^2 to the side surface area. A capped tube of volume 236.6 cm^3 and radius 3 cm, has a total surface area of 214.2 cm^2 = [157.7 cm^2] + [56.5 cm^2] = [(2 x 236.6 cm^3)/(3 cm)] + [6.28 x (3 cm)^2] = (2 x volume)/(radius) + [3.14 x (cylinder radius)^2].

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