Unit 28
PRISMS AND CYLINDERS:
VOLUMES, SURFACE AREAS, AND
WEIGHTS
PRISMS



A polyhedron is a three-dimensional (solid)
figure whose surfaces are polygons
A prism is a polyhedron that has two
identical (congruent) parallel polygon faces
called bases and parallel lateral edges
The volume of any prism is equal to the
product of the base area and the altitude
V  AB h where V  volume
AB  area of base
h  height
2
PRISMS

Prisms are named according to the shape of their
bases, such as triangular, rectangular, pentagonal,
and octagonal
Triangular Prism
Rectangular Prism
Pentagonal Prism Octagonal Prism
V  AB h where V  volume
AB  area of base
h  height
3
VOLUME OF A PRISM

Compute the volume of the fuel tank shown
in liters:
25 cm
60 cm
• V = ABh
• This prism has a rectangular base so
AB = length  width
AB = (60cm)(20cm) = 1200 cm2
• Now, V = ABh
= (1200 cm2)(25 cm)
= 30000 cm3
3
30000cm
x
1
1L
1000cm
3
 30Liters
4
CYLINDERS



A circular cylinder is a solid that has identical
circular parallel bases
The surface between the bases is called the
lateral surface.
The altitude (height) of a circular cylinder, is a
perpendicular segment that joins the planes of
the bases
Altitude
Lateral
Surface
(Sides)
5
CYLINDERS



The axis of a circular cylinder is a line that connects
the centers of the bases
In a right circular cylinder the axis is perpendicular to
the bases
The volume of right circular cylinders is the same as
prisms:
V = AB h
Right Circular Cylinder
Circular Cylinder
Axis
6
VOLUME OF A CYLINDER

Find the volume of the soup can shown below given
that the bases have a radius of 8 centimeters:
• V = ABh
16 cm
• The cylinder has a circular base, so
AB = r2 = (8)2 = 201.062 cm2
• Now, V = ABh
= (201.062 cm2)(16 cm)
= 3216.99 cm3 Ans
7
TRANSPOSING VOLUME FORMULAS

An engine piston has a height of 18.6
centimeters and a volume of 460 cubic
centimeters. Find the radius of the
piston:
– The piston is a circular cylinder, so V = ABh = r2h
– Substitute the given measurements into the formula
and solve for r:
V = r2h
460 cm3 = r2(18.6 cm)
r = 2.806 cm Ans
8
LATERAL AND SURFACE AREAS




The lateral area of a prism is the sum of the areas of
the lateral faces. The lateral area of a cylinder is the
area of the curved or lateral surface
The lateral area of a right prism equals the product of
the perimeter of the base and height
The lateral area of a right circular cylinder is equal to
the product of the circumference of the base and
height
The surface area of a prism or a cylinder equals the
sum of the lateral area and the two base areas
9
SURFACE AREA EXAMPLE

Find the surface area of the circular
cylinder trash can below given that it
has a radius of 8 inches:
– The surface area is equal to the sum of the
lateral area and the two base areas
40”
– Lateral area = CBh
= 2(8”)(40”)
= 2010.62 in2
– Area of base = r2
= (8”)2 = 201.062 in2
– Surface area = 2010.62 + 201.062 + 201.062
10
= 2412.744 in2 Ans
PRACTICE PROBLEMS
1.
2.
3.
4.
Find the volume of a mobile home (rectangular
prism) with a length of 10 meters, width of 15
meters, and height of 20 meters.
Determine the lateral area of the mobile home in
problem #1.
Compute the surface area of the mobile home is
problem #1.
Find the volume of a triangular prism given that the
triangular bases have sides of 8 inches, 10 inches,
and 12 inches and that the prism has a height of 5
inches.
11
PRACTICE PROBLEMS (Cont)
5.
6.
7.
8.
Compute the volume of the interior of a pen (right
circular cylinder) with a radius of 15 mm and a
height of 25 mm.
Find the lateral area of the pen in problem #5.
Find the surface area of the pen in problem #5.
Find the diameter of a circular culvert given that it
has a volume of 150 cubic feet and a height of 12.5
feet.
12
PRACTICE PROBLEMS (Cont)
9.
10.
A solid steel post 27.6 inches long has
a square base. The post has a volume
of 110 cubic inches. Compute the
length of a side of the base.
Find the lateral area of a box with a
length of 18 inches, width of 14
inches, and height of 12 inches.
13
PROBLEM ANSWER KEY
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
3000 m3
1000 m2
1300 m2
198.431 in3
17671.46 mm3
2356.19 mm2
3769.91 mm2
3.91 feet
1.996 inches
768 in2
14