3.5a: Surface Area of Prisms and
Cylinders
GSE’s
Primary
M(G&M)–10–6 Solves problems involving perimeter, circumference, or area of two dimensional figures
(including composite figures) or surface area or volume of three
Secondary
M(G&M)–10–2 Makes and defends conjectures, constructs geometric arguments, uses geometric properties, or
uses theorems to solve problems involving angles, lines, polygons, circles, or right triangle ratios (sine, cosine,
tangent) within mathematics or across disciplines or contexts (e.g., Pythagorean Theorem, Triangle Inequality
Theorem)
3-D figures- Solid figures. When the sides are polygons, its called a polyhedron.
Prism: a 3-D solid with 1) 2 bases – which are parallel and congruent
2) lateral faces that are parallelograms
* names by the shape of their bases
Base
Lateral Edge
Lateral Face – parallel sides not the base
Altitude (height)- Distance between the
bases
Base (parallel & Congruent)
Areas of the Solids
Lateral Area (LA) – the sum of the
areas of the lateral faces only.
– Does not include the area of the bases.
Surface Area (SA) – the sum of the
areas of ALL the faces.
– Lateral area + area of the bases
Ex: Find the lateral & surface
areas of the triangular prism.
10 in.
60o
 15.59
http://guilford.rps205.com/departments/Math/Links/Honors%20Geometry/Honors%20Geometry%20Power%20Points/12.2%20SA%20of%20Prisms%20&%20Cylinders.ppt#7
Find the Surface Area
Cylinders: 1) has 2 circular bases
2) bases are both parallel and congruent
Right cylinder –
the axis is the same as the altitude
Oblique CylinderThe axis is longer than the
altitude
altitude
axis
Find the surface area and lateral area
Example
A right cylinder has a surface area of 400 square mm.
Find the height of the cylinder
if the diameter of the base of the cylinder is 10 mm.
example2
If the side of a cube is doubled, what
happens to the surface area ?
Challenge
The Lateral Area of a right rectangular prism is 784 square cm.
Its length is three times its width.
Its height is twice its width.
Find the surface area.
Ex. 1 – Released Item from 2007 NECAP
A square with a side length of 8.0 cm is rolled up, without overlap, to
form the lateral surface of a cylinder.
What is the radius of the cylinder to the nearest tenth of a
centimeter?
Ex 2. Find the Surface Area
13 in
4 in
12 in
5 in
Describe the solid that is made from each of
these nets.
Prism
Describe the solid that is made from each of
these nets.
Cube
Describe the solid that is made from each of
these nets.
Pyramid
Complete the following net of a cube
Now complete the net in a different way
Complete the cuboid (rectangular prism) net
Which one of these nets can be folded to
make a cube?
Yes
(but with overlap)
No
Which one of these nets can be folded to
make a cube?
No
Yes
Complete the Net of this
Building
Scale: 1 square represents 1 m
Plan
Homework