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27 November, 08:02

a rectangular prism has a volume of 810 cubic meters. it has a length of 10 meters and a width of 9 meters. What is the height of the prism

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  1. 27 November, 10:47
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    The height of the prism is 9 meters

    Step-by-step explanation:

    * Lets describe the rectangular prism

    - The rectangular prism has six rectangular faces

    - Two of them are bases and the other four are side faces

    - The rectangular prism has three dimensions length, width, height

    - The volume of any prism = Area of the base * its height

    ∵ The base of the rectangular prism is a rectangle

    ∵ Area any rectangle = length * width

    ∴ The volume of the rectangular prism V = length * width * height

    * Lets solve the problem

    ∵ The volume of the prism is 810 meter³

    ∵ Its length is 10 meter

    ∵ Its width is 9 meters

    ∵ V = length * width * height

    - Substitute the values of the volume, the length and the width in

    the equation of V

    ∴ 810 = 10 * 9 * h

    ∴ 810 = 90 * h

    - Divide both sides by 90

    ∴ 9 = h

    ∴ The height of the prism is 9 meters
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