What Is a Lateral Cylinder & a Total Cylinder?

Lateral Cylinder

• The lateral cylinder is the curved part of the cylinder. If you are working with a tin can, a cylinder that is familiar to most people, the lateral cylinder is the sides of the can -- the tube you would have left after removing the circular top and circular bottom. If you cut along the seam and unroll this tube you would have a rectangle. One dimension of the rectangle is the height of the original can, and the other dimension is the circumference of the circular top or bottom of the can. The circumference of a circle is pi times the diameter of the circle. The area of the rectangle (the lateral cylinder) is equal to the length of the rectangle times the width of the rectangle. Area = length X width = height (of the cylinder) X circumference = height X diameter X pi. Pi is the ratio of any circle's circumference to its diameter, approximately 3.14159265.

End Pieces

• The top and bottom of a cylinder are both circles. The formula for a circle is: Area = pi X radius squared. This is often written A = pi X r^2. Because there are two end pieces the total area of the end pieces of a cylinder is A-total = 2 X pi X r^2.

Total Cylinder

• The total cylinder is the combined areas of the sides and ends. If you are using the radius, Total-Area = lateral cylinder + end areas = height X (2 X radius X pi) + 2 X pi X radius squared = 2 X pi X r (h + r).

Radius and Diameter

• The diameter is the distance across the circle at the widest point. The radius is the distance from the center of the circle to a point on the circumference. In some situations, it is preferable to work with the diameter of a circle -- where the radius is half the diameter. In the lateral case, Area = 2 X height X radius X pi. If you are working with the diameter (d) instead of the radius, the formula changes. A = pi X (d/2)^2 = pi X (d^2)/4 which is usually written A = 1/4 X pi X d^2. Because there are two end pieces the total area of the end pieces of a cylinder is A-total = 2 X pi X r^2 or A-total = 1/2 X pi X d^2. If you are using the diameter, Total-Area = lateral cylinder + end areas = height X (diameter X pi) + 1/4 X pi X diameter squared = pi X d (h + d/4).

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