Surface Area
Take a moment to think about how you could tackle the problem
below.
 If we wanted to paint the cabinets, how many cans of paint would
we need? The standard assumption is that a 1 gallon can will
cover about 350 ft2.
 How would you calculate this?
Using the supplies available, let’s work in groups to try and figure this
out!
Let’s see what our thoughts are for this problem.
Definitions:
 Surface Area
o The total area of the outside faces of a 3D object
Let’s have a look at a handout I have for you on the different objects we
need to be familiar with.
In this unit, you need to know several types of 3D objects and the key
measurements for each.
 Right Prism
o A 3D object whose sides are all flat and has the same cross
section along its entire length
o Key measurements: length (L), width (w) and height (h)
o Ex. Cube, Rectangular Prism, Triangular Prism
 Right Pyramid
o A 3D object with a flat base that is connected to triangular
sides that meet at a single point called the apex
o Key measurements: length (L), width (w), height (h), slant
length (sl), perimeter (P)
o Ex. Triangular Pyramid, Square Pyramid
 Right Cylinder
o A 3D object with circular ends and
a curved side
o Key measurements: radius (r),
height (h)
 Right Cone
o
A 3D object with a flat, circular
base and curved side that ends in a
point called the apex
o
Key measurements: radius (r),
height (h) and side length (s)
 Sphere
o A 3D object with no edges or corners
and all points on its surface are the
same distance from its center
o Key measurements: radius (r)
Surface Area Equations:
 Right Prism
𝑆𝐴 𝑜𝑓 𝑎 𝑅𝑖𝑔ℎ𝑡 𝑃𝑟𝑖𝑠𝑚 = 𝑆𝐴 𝑜𝑓 𝐸𝑛𝑑𝑠 + 𝑆𝐴 𝑜𝑓 𝑆𝑖𝑑𝑒𝑠
 Right Pyramid
1
𝑆𝐴 𝑜𝑓 𝑅𝑖𝑔ℎ𝑡 𝑃𝑦𝑟𝑎𝑚𝑖𝑑 (𝑠𝑎𝑚𝑒 𝑠𝑖𝑑𝑒𝑠) = 𝐵𝑎𝑠𝑒 𝐴𝑟𝑒𝑎 + 𝑃(𝑠𝑙)
2
𝑆𝐴 𝑜𝑓 𝑅𝑖𝑔ℎ𝑡 𝑃𝑦𝑟𝑎𝑚𝑖𝑑 (𝑑𝑖𝑓𝑓 𝑠𝑖𝑑𝑒𝑠) = 𝐵𝑎𝑠𝑒 𝐴𝑟𝑒𝑎 + 𝑆𝑖𝑑𝑒 𝐴𝑟𝑒𝑎𝑠
 Right Cylinder
𝑆𝐴 𝑜𝑓 𝑅𝑖𝑔ℎ𝑡 𝐶𝑦𝑙𝑖𝑛𝑑𝑒𝑟 = 2𝜋𝑟(𝑟 + ℎ)
 Right Cone
𝑆𝐴 𝑜𝑓 𝑅𝑖𝑔ℎ𝑡 𝐶𝑜𝑛𝑒 = 𝑆𝐴 𝑜𝑓 𝐵𝑎𝑠𝑒 + 𝑆𝐴 𝑜𝑓 𝑆𝑖𝑑𝑒
𝑆𝐴 𝑜𝑓 𝐵𝑎𝑠𝑒 = 𝜋𝑟 2
𝑆𝐴 𝑜𝑓 𝑆𝑖𝑑𝑒 (𝑖𝑓 𝑦𝑜𝑢 ℎ𝑎𝑣𝑒 𝑠) = 𝜋𝑟𝑠
𝑆𝐴 𝑜𝑓 𝑆𝑖𝑑𝑒 (𝑖𝑓 𝑦𝑜𝑢 ℎ𝑎𝑣𝑒 ℎ) = 𝜋𝑟√𝑟 2 + ℎ2
 Sphere
𝑆𝐴 𝑜𝑓 𝑆𝑝ℎ𝑒𝑟𝑒 = 4𝜋𝑟 2
Note: It is expected you know the area of many 2D shapes at this point,
but to help you out…
 Square/Rectangle
𝐴 = 𝐿𝑤 𝑜𝑟 𝐿ℎ 𝑜𝑟 𝑤ℎ
 Triangle
 Circle
1
𝐴 = 𝑤ℎ
2
𝐴 = 𝜋𝑟 2
Let’s try a few together:
 Find the surface area of the following objects
a) 804 cm2
c) 176 cm2
e) 534 ft2
 What is the side length of a cone whose radius is 6 m and surface
area is 320.44 m2?
(11 m)
Practice
Complete the Surface Area Practice handout.
Name:_______________ Date:_______________
Surface Area Practice
1. Find the surface area of each object below. Don’t let them scare
you. They are simply combinations of the basic objects we’ve
covered. You just need to problem solve a little.
2. Sketch each object and find the unknown measurement in each of
the following
a. A sphere has a surface area of 4536.46 cm2. What is its
radius?
b. A square pyramid has a 5 ft by 5 ft base. If the surface area is
99 ft2, what is the height of the pyramid?