A prism shaped solid whose bases are circles is a
cylinder. If the segment joining the centers of the circles of a cylinder is perpendicular to the planes of the bases, the cylinder is a
right circular cylinder. In Figure
1 , cylinder (a) is a right circular cylinder and cylinder (b) is an oblique circular cylinder.
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Figure 1
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Different types of circular cylinders.
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Lateral area, total area, and volume for right circular cylinders are found in the same way as they are for right prisms.
If a cylinder is pictured as a soup can, its lateral area is the area of the label. If the label is carefully peeled off, the label becomes a rectangle, as shown in Figure
2 .
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Figure 2
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The lateral area of a cylinder.
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The area of the label is the area of a rectangle with a height the same as the altitude of the can and a base the same as the circumference of the lid of the can.
Theorem 90: The lateral area,
LA, of a right circular cylinder with a base circumference
C and an altitude
h is given by the following equation.
Theorem 91: The total area,
TA, of a right circular cylinder with lateral area
LA and a base area
B is given by the following equation.
Theorem 92: The volume of a right circular cylinder,
V, with a base area
B and altitude
h is given by the following equation.
Example 1: Figure
3 is a right circular cylinder; find (a)
LA (b)
TA and (c)
V.
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Figure 3
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Finding the lateral area, total area, and volume of a right circular cylinder.
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Fundamental Ideas
Geometric Solids
