1. Geometry
12.3 Part 2
Cones

2. Right Cones

3. Oblique Cones

4. Right Cones Lateral area: L.A. Total area: T.A. Volume: V
Today you will learn how to find three measurements about right cones. You will find:
Lateral area: L.A.
Total area: T.A.
Volume: V

5. • Right Cone Vocabulary h r base one circle altitude joins the vertex
to the center of the base,
with length h h l
radius radius of the base is
also the radius of the
cone, r •
base r
slant height hypotenuse of a
right triangle formed
by the altitude and a
radius, l

6. Lateral Area of a Cone: L.A.
The lateral area of a cone equals half the circumference of the base times the slant height.
L.A = ½•2πr•l 10 8 •
L.A = πrl 6
which is
LA = π • 6 •10
= 60π square units

7. T.A = L.A. + B Total Area of a Cone: T.A. T.A. = πrl + πr²
The total area of a cone equals the lateral area plus the area of the base. 10
T.A = L.A. + B 8 • 6
which is
TA = 60π + (π • 6²)
= 60π + 36π
= 96π square units
T.A. = πrl + πr²

8. V = πr²h Volume of a Cone: V
The volume of a cone equals one third the area of the base times the height of the cone. 10
V = πr²h 8 • 6
V = 1/3 • π • 6² • 8
= 96π cubic units

9. Exercises 1. radius: 3 height: 4 slant height(l): ______ 5 4
Find the missing information. 1.
radius: 3
height: 4
slant height(l): ______
Lateral Area: ______
Total Area: ______
Volume: _____
1. (a)
LA = πrl 5 4
LA = π • 3 •5 5
LA = 15π un² 3
15π
(b) TA = LA + B
24π
TA = 15π + π•3²
12π
TA = 15π + 9π
TA = 24π un²
(c) V = 1/3πr²h
V = 1/3 • π • 3² • 4
= 12π un³

10. Exercises 2. slant height: 10 10 8 radius: 6 height:
Find the missing information.
1. (a)
LA = πrl 2.
slant height: 10
radius: 6
height:
Lateral Area: ______
Total Area: ______
Volume: _____ 10 8
LA = π • 6 • 10
LA = 60π un² 6 8
(b) TA = LA + B
60π
TA = 60π + π•6²
96π
TA = 60π + 36π
96π
TA = 96π un²
(c) V = 1/3πr²h
V = 1/3 • π • 6² • 8
= 96π un³

11. Exercises 3. radius: 5 Total Area: 90 cm2 Volume: _____ 13 12 5
Find the missing information.
1. (a)
LA = πrl 3.
radius: 5
Total Area: 90 cm2
Volume: _____ 13 12
65π = π • 5 • l
l = 13 un 5
h = 12 un
100π
Base area = π • 5² = 25π
(c) V = 1/3πr²h
LA = TA - B
= 90π - 25π = 65π
V = 1/3 • π • 5² • 12
= 100π un³

12. Homework -P. 492 WE #1-19 odd, #22 calc.
-Bring Your Compass for tomorrow!!