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The Cuboid


rectangular prism



The cuboid is also referred to as a rectangular prism. If your student does not understand why a cube, is also a prism I highly recomend you go to our explanation first.

To be comfortable calculating volume and surface area, your child should be comfortable with multiplication as well as addition.


Surface Area of Cuboid

surface area formula
We know that a cuboid is made up of six rectangular faces.
We also know that these six faces come in three pairs.

Looking at the image to the left we can see the:
area of the front face is b x h (bh)
This is the same as the area of the back face so we multiply it by 2 - 2bh
We can see the area of the side face is l x h (lh)
This is the same as the other side of the cuboid so we multiply it by 2 - 2lh
We can see the area of the bottom face is l x b (lb)
This is the same as the top face, so we multiply it by 2 - 2lb

The surface area is the area of all the shapes making the three dimensional shape, so we must add all these areas together:

2lh + 2lb + 2bhUnits Squared



Volume of a Cuboid

volume formula
Looking at this image, we can see that there are three individual measurements on a cuboid.
  • Length
  • Breadth/Width
  • Height


The volume is:
Length x Breadth x Height
or to abbreviate it further:
V = lbhUnits Cubed






Return from this page on the Cuboid to our other 3d Geometric Shapes
or
Return to our k6 geometric shapes home page to explore more great basic geometry






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