A
right circular cone is similar to a regular pyramid except that its base is a circle. The vocabulary and equations pertaining to the right circular cone are similar to those for the regular pyramid. Refer to Figure
1 for the vocabulary regarding right circular cones.
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Figure 1
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A right circular cone.
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Theorem 96: The lateral area,
LA, of a right circular cone with base circumference
C and slant height
l is given by the following equation.
Theorem 97: The total area,
TA, of a right circular cone with lateral area
LA and base area
B is given by the following equation.
Theorem 98: The volume,
V, of a right circular cone with base area
B and altitude
h is given by the following equation.
Example 1: Figure
2 is a right circular cone; find (a)
LA (b)
TA and (c)
V.
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Figure 2
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Finding the lateral area, total area, and volume of a right circular cone.
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- (a)
The slant height, radius, and altitude of a right circular cone form a right triangle, as shown in Figure
3 .
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Figure 3
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The right triangle formed by the slant height, radius, and altitude of a right circular cone.
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- (b)
- (c)