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Popcorn Prisms
Surface Area
& Volume
To do the next two lessons, you
need to know...
•That a prism is a 3-dimensional
shape with 2 identical parallel
bases.
•The formulas for SA (surface
area) and for V (volume) of a
rectangular prism and a cylinder.
Let’s start in the beginning…
Before you can do surface area or
volume, you have to know the following
formulas.
Rectangle
A = lw
Circle
A = πr²
C = πd
Let’s start with a rectangular prism.
Surface area can be done using the formula
SA = 2 lw + 2 lw + 2 lw
you can find the area
OR
for each surface and
add them up.
Either method will give you the same answer.
Volume of a rectangular prism is V = lwh
Example:
7 cm
4 cm
Surface Area
8 cm
Front/back 2(8)(4) = 64 cm²
Left/right
2(4)(7) = 56 cm²
Top/bottom 2(8)(7) = 112 cm²
Add them up!
SA = 232 cm²
Volume
V = lwh
V = 8(4)(7)
V = 224 cm³
CIRCLES
You must know the difference
between RADIUS and
DIAMETER.
Center of the circle
r
d
SURFACE AREA of a CYLINDER.
Imagine that you
can open up a
cylinder like so
You can see
that the surface
is made up of
two circles and
a rectangle.
The length of the rectangle is the
same as the circumference of the
circle!
EXAMPLE: Round to the nearest TENTH.
Top or bottom circle Rectangle
A = πr²
C = length
A = π(3.1)²
C=πd
A = π(9.61)
C = π(6.2)
A = 30.2 cm²
C = 19.5 cm
Now add:
30.2 + 30.2 + 234 =
Now the area
A = lw
A = 19.5(12)
A = 234 cm²
SA = 294.4 in²
There is also a formula to find surface area of a cylinder.
Some people find this way easier:
SA = 2πrh + 2πr²
SA = 2π(3.1)(12) + 2π(3.1)²
SA = 2π (37.2) + 2π(9.61)
SA = π(74.4) + π(19.2)
SA = 233.7 + 60.4
SA = 294.1 in²
The answers are REALLY close, but not exactly the
same. That’s because we rounded in the problem.
Find the radius and height of the cylinder.
The formula tells you what to do!!!!
Remember the order of operations. You
multiply before you add.
2πrh + 2πr² means
multiply 2(π)(r)(h) + 2(π)(r)(r)
Volume of a Cylinder
We used this drawing for our
surface area example. Now we
will find the volume.
V = (πr²)(h)
V = (π)(3.1²)(12)
optional
step!
V = (π)(3.1)(3.1)(12)
V = 396.3 in³
ARE YOU READY?
Let’s see what you can do with
POPCORN PRISMS!
YUM!!