Section 12.4 & 12.5

Volume of Prisms & Cylinders Volume of Pyramids & Cones Go over Quizzes

Volume of Prisms and Cylinders

What physical process did we relate to surface area?

What about volume?

Formula for the Volume of a Prism and Cylinder

Prism Cylinder

V Bh V Bh

2V r hREMEMBER:

B – represents the area of

one base

h – represents the height of

the prism or cylinder

cross section

Example 1: A triangular prism has a height of 10 cm. The lengths of the base edges are 13 cm, 24 cm, and 13 cm. Find the volume.

V Bh

1V 24 5 10

2

3V 600 cm

Volume of Pyramids & Cones

Pyramid

Cone

D D

H H

1V Bh

3

21V r h

3

1V Bh

3

Example 2: Find the volume. The lateral faces are rectangles.

12 mm

4 mm

6 mm

3 5 mm

6 mm

1V 12 6 6 4

2

V Bh

3V 216 mm

Example 3: Find the volume of the pyramid with a base that is a rhombus. The diagonals of the rhombus are 7 and 6.

5

1

V Bh3

1 1V 7 6 5

3 23V 35 u

Example 4: Find the volume of the frustum.

14 mm

68 mm

6 mm

2 2big big small small

1 1V r h r h

3 3

2 21 68 1 14V 34 7

3 9 3 9

78608 686V

27 27

77922V

27

V 2886

34 7

x 6 x

14

x9

On your own: Find the volume.

60o

12 cm

(1) (2) A square pyramid has a lateral edge of 13 and a base diagonal of 10.

(3)9 mm

12 mm

ANSWERS:

31) 72 3 cm

33) 243 mm

32) 200 u

Triangular Prism