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 cylinder’s 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 sphere’s radius

10. Example 1
Find the total area of the figure 6 5

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