12-5 and 12-6 Volumes of Prisms, Cylinders, Pyramids, and Cones

Objective – Find the volumes of prisms, cylinders, pyramids, and cones.

Prism

Volume of a Prism

BhV Volume

HeightBase Area

h

Base Area

Remember the “Base Area” formula will be determined by the base shape.

Find the volume of the rectangular prism.

BhV

wlB

1513B

2195unitsB

12195V3m 2340V

#1 Finding the Volume of a Prism

12

1315

#2 example

Find the volume of the triangular prism.

12 cm

5 cm

3 cm 4 cm

BhV

bhB2

1 )12(6V

3cm 72V

5 cm

3 cm

222 53 h

h 259 2 h162 h

4h

)4)(3(5.0B2cm 6B

Radius

Cylinder

Volume of a Cylinder

BhV Volume Height

2rB Base Area

Radius

Base Areah

Base Area

#3 Finding the Volume of a Cylinder

10 cm

5 cm

BhV

Find the volume of a cylinder with height 10 cm and radius 5cm.

2rB 2)5(B

2cm 25B)10(25V

3cm 250V

Theorem 10-8

Volume of a Pyramid

BhV3

1

VolumeHeightBase Area

B

#5 Finding Volume of a Pyramid Find the volume of a square pyramid

with base edges 5 m and height 3 m.

m 3

m 5

BhV3

1

)3)(25(3

1V

2sB 25B

2m 25B

3m 25V

Theorem 10-9

Volume of a Cone

BhV3

1

VolumeHeight

Base Area

rB

#6 Finding the Volume of a Cone

The radius of the base of a cone is 6 m. Its height is 13 m. Find the volume.

m 6

BhV3

1

)13)(36(3

1 V

2rB 26B

2m 36B

3m 156V

m 13

Homework

Page 668 5 – 10

Page 675 5 – 10

#4 Finding the Volume of a Cylinder

9 ft

6 ft

BhV

Find the volume of the cylinder.

2rB 2)6(B

2ft 36B)9(36V3ft 324V