Cylinders and Cones

1
Cylinders and Cones

• Lesson 12 -3

2
Cylinder

• Like a prism
• Bases are circles instead of polygons.
• Formulas for the area and volumes of cylinders
  are similar to prisms.
• REMEMBER C 2pr A pr²

h
Right cylinder
r
3
Theorems!

• The lateral area of a cylinder equals the
  circumference of a base times the height of the
  cylinder.
• L.A. 2prh

8
6
L.A. 2 p 8 6 2 48 p
96p
4

• The total area of a cylinder is the lateral area
  plus twice the area of a base.
• T.A. L.A. 2B

8
6
T.A. 96p 2(p 6²) 96p 72p
168p (cm²)
5

• The volume of a cylinder equals the area of a
  base times the height of a base times the height
  of the cylinder.
• V Bh pr²h

8
6
V pr²h p 6² 8 288p (cm³)
6
Individual Practice!

• 1. r 5 h 8

2. r 6 h 9
L.A. 2 p 6 9 2 54 p
108p
L.A. 2 p 5 8 2 40 p
80p
T.A. 108p 2(p 6²) 108p 72p
180p
T.A. 80p 2(p 5²) 80p 50p
130p
V pr²h p 6² 9 324p
V pr²h p 5² 8 200p
7

• 3. r 5 h 4

4. r 3 h 7
L.A. 2 p 5 4 2 20 p
40p
L.A. 2 p 3 7 2 21 p
42p
T.A. 40p 2(p 5²) 40p 50p
90p
T.A. 42p 2(p 3²) 42p 18p
60p
V pr²h p 5² 4 100p
V pr²h p 3² 7 63p
8

• 5. L.A. 96p h 12

Find r L.A. 2prh
96p 2 p r 12 96p 24p r 96p 24p
4 r
6. V 375p h 15
Find L.A. V Bh
375p pr²h 375p p r² 15 375p 15p ?25
5 r
L.A. 2 p 5 15 2 75 p
150p
9

• 7. L.A. 96p r 8

Find r (L.A. 2prh) (V Bh)
96p 2 p 8 h 96p 16p h 96p 16p 6
h
V pr²h p 8² 6 384p
8. T.A. 256p (cm²) r h
Find r T.A. L.A. 2B
256p 2prh 2(p r²) 256p 2p r h 2p
r² 256p 4p ?64 8 r
10
Cones

• Similar to a pyramid, but w/circle base
• Slant height is the hypotenuse of a right
  triangle formed by the altitude and radius.

11
The lateral area of a cone equals half the
circumference of the base times the sl. Height
(l).

• L.A. ½ 2pr l prl

The total area of a cone equals the lateral area
plus the area of the base.

• T.A. L.A. B prl pr²

The volume of a cone equals one-third of the base
times the height of the cone.

• V ?Bh ?pr²h

12
Example

• l 13 h 12

13
12² r² 13² 169 144 25 r 5
12
r
L.A. ½ 2pr l prl p 5 13
65p
T.A. L.A. B prl pr² 65p p
(5²) 90p
V ?Bh ?pr²h ?p 5² 12 100p
13
Individual Practice

• 9. r 3 l 5

h² 3² 5² 25 9 16 h 4
L.A. ½ 2pr l prl p 3 5
15p
V ?Bh ?pr²h ?p 3² 4 12p
T.A. L.A. B prl pr² 15p p
(3²) 24p
14
Individual Practice

• 10. r 10 h 24

24² 10² l² 576 100 676 l 26
L.A. ½ 2pr l prl p 10
26 260p
V ?Bh ?pr²h ?p 10² 24 800p
T.A. L.A. B prl pr² 260p p
(10²) 360p
15
Spheres

• Lesson 12-4

16
Spheres

• Area of a sphere equals 4p times the square of
  the radius.
• A 4pr²
• Volume of a sphere equals 4/3p times the cube of
  the radius.
• V 4/3pr³

17
Example r 5

• A 4pr²
• 4p 5²
• 100p

V 4/3pr³ 4/3p 5³ 166 2/3p
(or) 167p (or) 500/3p
18
Individual Practice

• 1. r 3

2. r 6
A 4pr² 4p 3² 36p
A 4pr² 4p 6² 144p
V 4/3pr³ 4/3p 6³ 288p
V 4/3pr³ 4/3p 3³ 36p
19

• 6. A 576p

7. V 137 2/3p
A 4pr² 576 4p r² 144 r² 12 r
V 4/3pr³ 1372/3 4/3p r³ 6.8 7 r
A 4pr² 4p 7² 196p
V 4/3pr³ 4/3p 12³ 2304p