2D and 3D Shapes
Food Truck Designers
How can we calculate volume and surface area?
by
Objectives:
We will be able to…
We will be able to…
calculate surface area
calculate volume
design and build a food truck
What 3D shapes can you find?
Turn and tell your partner what you see!
Rectangular
prism
Triangular prism
Cylinder
Cube
Food trucks are FULL of 3D shapes!
From shapes to measurements
Designers also need to know…
From shapes to measurements
These measurements are…
Volume
Surface area
Let’s take a closer look at
volume and surface area!
Volume
The amount of space inside a 3D object.
length
Width
Height
Length
x
x
width
height
Formula:
Let’s calculate volume!
When we have a composite 3D shape, we break the shape apart!
11 ft
3 ft
5 ft
6 ft
3 ft
5 ft
6 ft
6 ft
4 ft
4 ft
4 ft
Let’s calculate volume!
Now, we can solve for the volume of each shape and add them back together!
3 ft
5 ft
6 ft
6 ft
4 ft
4 ft
V = length x width x height
V = length x width x height
V= 6 x 4 x 3
V= 72 ft3
V= 5 x 4 x 6
V= 120 ft3
=
192 ft3
+
Surface Area
The total area covering the outside of an object
Formula:
width
height
(length x width)(2)
+
length
(height x width)(2)
+
(height x length)(2)
Let’s calculate surface area!
Like volume, we have to deconstruct our composite shape.
3 ft
3 ft
11 ft
6 ft
5 ft
4 ft
6 ft
5 ft
4 ft
4 ft
6 ft
Let’s calculate surface area!
Now, we need to calculate the surface area of each shape, THEN subtract the overlapping or hidden faces!
Turn and tell your partner: Where is the hidden face?
3 ft
3 ft
11 ft
6 ft
5 ft
4 ft
6 ft
5 ft
4 ft
4 ft
6 ft
Let’s calculate surface area!
Now, we need to calculate the surface area of each shape, THEN subtract the overlapping or hidden faces!
Area of faces -
Overlapping faces
3 ft
3 ft
11 ft
6 ft
5 ft
4 ft
6 ft
5 ft
4 ft
4 ft
6 ft
(3x6)(2) + (6x4)(2) + (3x4)(2)
+
(5x4)(2) + (4x6)(2) + (5x6)(2)
-
(4x3)
Let’s calculate surface area!
(3x6)(2) + (6x4)(2) + (3x4)(2)
(5x4)(2) + (4x6)(2) + (5x6)(2)
+
-
(4x3)
36
+
48
+
24
+
40
+
+
-
48
60
12
256
-
12
244 ft2
What about the wheels?
Let’s look at the formulas for surface area
and volume of cylinders!
Surface area | Volume |
A=2πrh+2πr2 | V= πr2h |
Food Truck Design Challenge
Today, you will be…
…your own food truck!
building
measuring
designing
and
Step 1: Design
What 3D shapes will make up your food truck?
What food will you sell?
Step 2: Build
Grab your cardboard
Draw any shapes you need to cut out
Cut out your shapes and designs using the ChompSaw!
Tape and hot glue your food truck together
Materials
Step 3: Measure and Calculate
Measure and record each dimension of your food truck.
Use those measurements to solve for surface area and volume!
Food Truck Expo
Designers show off their work!
Walk around the room and examine other food truck designs.
Record your observations on your Food Truck Expo worksheet!
Record your observations on the Food Truck Expo sheet.
Show What You Know!
You’re a mathematician!
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You have
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“Food Truck Designers!”