MTH 232
Section 10.4
Volume
Overview
• In this section we examine finding volume of
several three-dimensional figures.
• It is important to note that volumes are
expressed in cubic units, while areas are
expressed in square units.
Prisms and Cylinders
V  Bh
Where B is the area of the base and h is the height of the prism or
cylinder.
Pyramids and Cones
1
V  Bh
3
Where B is the area of the base and h is the height of the pyramid or
cone.
That’s base with a capital B
• Finding the area of a base depends on the
shape of that particular base.
• Your two-dimensional formula sheet lists the
area formulas for several different planar
figures.
Spheres
4 3
V  r
3
Where r is the radius of the sphere.
A word about pi.
• Pi is an irrational number that represents the ratio of
the circumference of a circle to its diameter.
• Because pi is irrational, when expressed as a decimal it
does not terminate (1/2 = 0.5) or repeat (1/3 =
0.33333……………., or 0.3
• Some commonly used approximations for pi include:
3.14 and 22/7.
• When students give answers for which pi was involved
in the calculation, they may either express their answer
in terms of pi (exact) or in terms of the numeric value
obtained by using an approximation of pi
(approximate).
Examples
• 2(a); 2(d); 3(a); 3(d); 5