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Cylinders and Cones
Lesson 12.3
Pre-AP Geometry
Lesson Focus
Four theorems are stated that give formulas for finding the
lateral area and volume of both cylinders and cones.
Basic Terms
Cylinder
The surface formed by the points at a fixed distance from a
given straight line. The solid enclosed by this surface and by
two planes perpendicular to the axis is also called a cylinder.
Cone
A three-dimensional geometric shape that tapers smoothly
from a flat, round base to a point called the vertex.
Cylinder
Theorem 12-5
The lateral area of a cylinder equals the circumference of a
base times the height of the cylinder.
LA = 2πrh
Theorem 12-6
The volume of a cylinder equals the area of a base times the
height of the cylinder.
V = πr2h
Cone
Theorem 12-7
The lateral area of a cone equals half the circumference of the
base times the slant height.
LA = 2πrℓ/2 = πrℓ
Theorem 12-8
The volume of a cone equals one third the area of the base
times the height of the cone.
V = πr2h/3
Practice
1. Determine the lateral area, total area, and volume of a right
cylinder with radius 5 and height 10.
2. Determine the slant height, lateral area, total area, and
volume of a right cone with radius 5 and height 12.