OBJECTIVEAFTER STUDYING THIS SECTION, YOU WILL BE ABLE TO FIND THE SURFACE
AREAS OF CIRCULAR SOLIDS
12.3 Surface Areas of Circular Solids
Cylinders
A cylinder resembles a prism in having two congruent parallel bases. The bases are circles.
If we look at the net of a cylinder, we can see two circles and a rectangle.
The circumference of the circle is the length of the rectangle and the height is the width.
Theorem
The lateral area of a cylinder is equal to the product of the height and the circumference of the base
where C is the circumference of the base, h is the height of the cylinder, and r is the radius of the base.
. . 2cylL A Ch rh
Definition
The total area of a cylinder is the sum of the cylinder’s lateral area and the areas of the two bases.
. . . . 2cyl baseT A L A A
Cone
A cone resembles a pyramid but its base is a circle. The slant height and the lateral edge are the same in a cone.
Slant height (italicized l)height
radius
Theorem
The lateral area of a cone is equal to one-half the product of the slant height and the circumference of the base
where C is the circumference of the base, l is the slant height, and r is the radius of the base.
1. .
2coneL A Cl rl
Definition
The total area of a cone is the sum of the lateral area and the area of the base.
. . . .cone baseT A L A A
Sphere
A sphere is a special figure with a special surface-area formula. (A sphere has no lateral edges and no lateral area).
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