How to Find The Height Of a Prism
Set up the formula for the volume of a prism., Plug the volume into the formula., Find the area of the base., Plug the area of the base into the volume of a prism formula., Solve the equation for h{\displaystyle h}.
Step-by-Step Guide
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Step 1: Set up the formula for the volume of a prism.
The volume for any prism can be found by using the formula V=Ah{\displaystyle V=Ah},where V{\displaystyle V} equals the volume of the prism, A{\displaystyle A} equals the area of one base, and h{\displaystyle h} equals the height of the prism.
The base of a prism is one of its congruent sides.
Since all opposite sides of a rectangular prism are congruent, any side can be used as the base, as long as you are consistent in your calculations. -
Step 2: Plug the volume into the formula.
If you do not know the volume, you cannot use this method.
For example, if you know the volume of the prism is 64 cubic meters (m3{\displaystyle m^{3}}), then your formula will look like this:64=Ah{\displaystyle 64=Ah} , To find the area, you need to know the length and width of the base (or of one side, if the base is a square).
Use the formula A=lw{\displaystyle A=lw}.
To find the area of a rectangle.
For example, if the base is a rectangle with a length of 8 meters and a width of 2 meters, to find the area you would calculate:
A=(8)(2){\displaystyle A=(8)(2)}A=16m2{\displaystyle A=16m^{2}} , Make sure you are substituting for the variable A{\displaystyle A}.
For example, if you found the area of the base to be 16 square meters, then your formula will look like this:64=16h{\displaystyle 64=16h} , This will give you the height of your prism.
For example, if your equation is 64=16h{\displaystyle 64=16h}, you would need to divide each side by 16 to find h{\displaystyle h}.Thus:6416=16h16{\displaystyle {\frac {64}{16}}={\frac {16h}{16}}}4=h{\displaystyle 4=h}So, the height of your rectangular prism would be 4 meters. -
Step 3: Find the area of the base.
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Step 4: Plug the area of the base into the volume of a prism formula.
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Step 5: Solve the equation for h{\displaystyle h}.
Detailed Guide
The volume for any prism can be found by using the formula V=Ah{\displaystyle V=Ah},where V{\displaystyle V} equals the volume of the prism, A{\displaystyle A} equals the area of one base, and h{\displaystyle h} equals the height of the prism.
The base of a prism is one of its congruent sides.
Since all opposite sides of a rectangular prism are congruent, any side can be used as the base, as long as you are consistent in your calculations.
If you do not know the volume, you cannot use this method.
For example, if you know the volume of the prism is 64 cubic meters (m3{\displaystyle m^{3}}), then your formula will look like this:64=Ah{\displaystyle 64=Ah} , To find the area, you need to know the length and width of the base (or of one side, if the base is a square).
Use the formula A=lw{\displaystyle A=lw}.
To find the area of a rectangle.
For example, if the base is a rectangle with a length of 8 meters and a width of 2 meters, to find the area you would calculate:
A=(8)(2){\displaystyle A=(8)(2)}A=16m2{\displaystyle A=16m^{2}} , Make sure you are substituting for the variable A{\displaystyle A}.
For example, if you found the area of the base to be 16 square meters, then your formula will look like this:64=16h{\displaystyle 64=16h} , This will give you the height of your prism.
For example, if your equation is 64=16h{\displaystyle 64=16h}, you would need to divide each side by 16 to find h{\displaystyle h}.Thus:6416=16h16{\displaystyle {\frac {64}{16}}={\frac {16h}{16}}}4=h{\displaystyle 4=h}So, the height of your rectangular prism would be 4 meters.
About the Author
Janet Rivera
Specializes in breaking down complex organization topics into simple steps.
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