1. 10-6 Volume of Prisms & Cylinders
Geometry

2. EXPLORING VOLUME
The volume of a solid is the number of cubic units
contained in its interior. Volume is measured in cubic
units, such as cubic meters (m3).

3. EXPLORING VOLUME VOLUME POSTULATES s The volume of a cube is the cube
of the length of its side, or V = s3.
Volume Congruence Postulate
If two polyhedra are congruent, then they have the
same volume.
Volume Addition Postulate
The volume of a solid is the sum of the
volumes of all its nonoverlapping parts.

4. Example 1 Find the volume of the Cube with edge length 15 in.
#3 on pg. 746

5. FINDING VOLUMES OF PRISMS AND CYLINDERSh B B B h r
VOLUME THEOREMS
Volume of a Prism
The volume V of a prism is V = B h, where
B is the area of a base and h is the height.
Volume of a Cylinder
The volume V of a cylinder is V = B h = r 2 h, where
B is the area of a base, h is the height, and
r is the radius of a base.

6. Ex. 2 Find the volume of the right rectangular prism
5 cm
3 cm
13 cm

7. Ex. 3 Find the volume of the right hexagonal prism

8. Example 4
Find the volume of the oblique cylinder. Give your answers in terms of & rounded to the nearest tenth.
14 in.
18 in
EX. Ex. 2

9. Ex. 5
Find the volume of the cylinder with the base area cm² & a height equal to twice the radius. Give your answers in terms of & rounded to the nearest tenth.

10. Assignment

11. Example 3 Use the measurements given to solve for x.
a) Rectangular prism, V=396
b) Right cylinder, V=277
Diameter = x ft, height = 5ft

12. Using Volumes in Real Life
0.66 ft
1.31 ft
0.39 ft
0.33 ft
The area of the base can be found as follows:
CONSTRUCTION Concrete weighs 145 pounds per cubic foot. To find the weight of the concrete block shown, you need to find its volume.
Area of large
rectangle
Area of small
rectangle
B =
– 2 •
= (1.31) (0.66) – 2(0.33) (0.39)
 0.61 ft 2
Using the formula for the volume of a prism, the volume is
V = Bh
 0.61(0.66)
 0.4 ft 3.

13. Using Volumes in Real Life
To find the weight of the block, multiply
the pounds per cubic foot, 145 lb/ft 3, by
the number of cubic feet, 0.40 ft 3.
114 lb
1 ft 3
• 0.4 ft 3
Weight =
 58 lb

14. Example 4
Find the volume of the entire solid. The prisms and cylinders are right.
#37 Pg. 748

15. FINDING VOLUMES OF PRISMS AND CYLINDERS
THEOREM
Theorem Cavalieri’s Principle
If two solids have the same height and the same
cross-sectional area at every level, then they have
the same volume.