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).

Postulate

where r is the sphere’s radius

2. . 4sphereT A r

Example 1

Find the total area of the figure

5

6

Example 2

Find the total area of the figure

5

6

Example 3

Find the total area of the figure

5

Summary

Explain in your own words how to find the surface area of a cylinder?

Homework: worksheet