To find the volume of the prism the
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area
of the triangular base is multiplied by the
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height
of the prism or
Interactive popup. Assistance may be required._______________V = B∙h =(12b∙h)∙h
.
If the base of the prism is a hexagon, the volume is still found using the formula V = B∙h.
Example
A builder is building a house that will sit 4 feet above ground on concrete support pilings that are buried 2 feet into the ground. The concrete will be poured into wooden forms that are in the shape of hexagonal prisms. The builder must know the amount of concrete to buy in order to have enough to pour the pilings. His sketch is shown below.
How many cubic feet of concrete must the builder order in order to fill 20 pilings like the one show in his sketch?
Answer the following questions. Click on the blank space to check your answers.
The formula for volume is
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where
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is the area of the hexagonal base.
The area of the
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hexagonal
base is found by using the area of a triangle.
The base is made up of
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6
equilateral triangles.
The formula for the area of a triangle is
Interactive popup. Assistance may be required._______________A = 12bh
where b and h are the base and height of one equilateral triangle.
The area of the hexagonal base can be found using the formula
Interactive popup. Assistance may be required._______________B = 6(12bh)
.
The area of the hexagonal base is
Interactive popup. Assistance may be required._______________B = 6(12bh) = 6(12∙ 6 ∙ 4) = 6(12) = 72 sq in
.
The problem is asking for the cubic feet of concrete needed to fill the hexagonal prism. The
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The base is in square
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inches
and the height is
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feet
.
The height needs to be converted into
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inches
Six feet equals
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6 x 12 = 72 inches
Therefore h, the height of the prism, is
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72 inches
.
Find the volume by substituting the values into the formula
The builder needs to purchase enough cement to pour 20 pilings. Cement is measured in cubic feet.
The volume needs to be converted from
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cubic inches
to
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cubic feet
.
There are
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12 inches
in one foot.
There are
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12 x 12 x 21 = 1728
cubic inches in one cubic foot.
To change the volume from cubic inches to cubic feet
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divide
the volume by 1728 cubic inches.
One piling is
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5184 ÷ 1728 = 3
cubic feet.
The builder needs 20 pilings, each piling requires
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3 cubic feet
of concrete.
The builder will need
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3 x 20 = 60
cubic feet of concrete.
Watch a video of more examples of finding the volume of prisms.
Source: Volume of a Triangular Prism, mrksclass, YouTube