OBJECTIVE

1
12.3 Surface Areas of Circular Solids

• OBJECTIVE
• AFTER STUDYING THIS SECTION, YOU WILL BE ABLE TO
  FIND THE SURFACE AREAS OF CIRCULAR SOLIDS

2
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.

3
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.

4
Definition

• The total area of a cylinder is the sum of the
  cylinders lateral area and the areas of the two
  bases.

5
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
6
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.

7
Definition

• The total area of a cone is the sum of the
  lateral area and the area of the base.

8
Sphere

• A sphere is a special figure with a special
  surface-area formula. (A sphere has no lateral
  edges and no lateral area).

9
Postulate

• where r is the spheres radius

10
Example 1

• Find the total area of the figure

6
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11
Example 2

• Find the total area of the figure

6
5
12
Example 3

• Find the total area of the figure

5
13
Summary

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