objective after studying this section, you will be able to find the surface areas of circular solids...
TRANSCRIPT
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).