VocabularyCubic units: Units used and designed to measure volume. We can tell something is a "cubic unit" when it has the small ³ above it.
Volume: Volume is the space within a 3-Dimensional Shape. Surface Area: Surface Area is the space around a 3-Dimensional Shape 3-Dimensional Objects: 3-Dimensional shapes are shapes that have length width and depth. |
Today's Target: Be introduced to Volume and Surface area, and be able to calculate the volume of Rectangular prisms.
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The Formulas
Cubes: Length³
Rectangular Prisms: Area (of rectangle) x Depth
Triangular Prisms: Area (of triangle) x Depth
Cylinders: Area (of circle) x Depth
Ultimately, the formula for calculating many 3D shapes is the original area of the 2D shape times the depth of the shape.
Two 3D shapes have unique formulas. You do not need to commit these to memory now, but be aware these have unique formulas.
Sphere: (4 ÷ 3) × π × r^3
Cones: (1 ÷ 3) x π × r^2 x h
Those two look more intimidating than they actually are.
But don't worry, we're not practicing those just yet.
Rectangular Prisms: Area (of rectangle) x Depth
Triangular Prisms: Area (of triangle) x Depth
Cylinders: Area (of circle) x Depth
Ultimately, the formula for calculating many 3D shapes is the original area of the 2D shape times the depth of the shape.
Two 3D shapes have unique formulas. You do not need to commit these to memory now, but be aware these have unique formulas.
Sphere: (4 ÷ 3) × π × r^3
Cones: (1 ÷ 3) x π × r^2 x h
Those two look more intimidating than they actually are.
But don't worry, we're not practicing those just yet.
What is Volume?
The volume of an object is the space within a 3-Dimensional shape. A cup has volume, your phone has volume, you have volume. Essentially, volume is really the literally space within a 3-Dimensional object. Volume is incredibly important in our world because volume is all about 3-Dimensional shapes.
If you want to design games, build houses, print 3D objects, or know how much space is in a fridge, being able to understand volume is important. |
What is Surface Area
On a 3D object, surface area would be considered the perimeter. It is the total area around the shape.
If you had beach ball, the surface area would just be the outer layer of the ball that you see. Surface area and Volume are the two important key terms when understanding 3D shapes. Calculating the surface area means finding each Area and adding all totals together. We will be looking at Surface area in a future lesson lesson. |
Example - Volume
To find the volume, multiply Width and Length together to find the Area
Now, you could have done the multiplying in a different order. As long as you find the Area of one side of the 3D object, then multiply your result by the opposing number (the depth) you will receive the same result.
- Volume = Area x Depth
- V = 35 x 4
- V = 140
Now, you could have done the multiplying in a different order. As long as you find the Area of one side of the 3D object, then multiply your result by the opposing number (the depth) you will receive the same result.
Live Examples
I will be modelling the examples with your input now, follow along with a paper/pencil.
Questions
The following are rectangular prisms. Work to solve the Volume of these shapes.