Solving for the Height of a Cuboid Using Volume and Base Area

Introduction to Volume and Base Area Relationship

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In geometry, the volume and base area of a cuboid are two essential dimensions that can be used to determine other unknowns, such as the height of the cuboid. This article will delve into the process of solving for the height of a cuboid given its volume and base area. The relationships between these dimensions are crucial for many practical applications in mathematics, science, and engineering.

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Understanding the Basic Formula

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The formula that links the volume of a cuboid to its base area is quite straightforward:

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Volume Base Area × Height

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This fundamental equation can be rearranged to solve for the height:

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Height Volume / Base Area

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Example Calculation

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Given a cuboid with a volume of 168 cubic meters (m3) and a base area of 28 square meters (m2), we will use the formula to calculate the height.

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Step 1: Write down the given values.

" "" "Volume 168 m3" "Base Area 28 m2" "" "

Step 2: Substitute the values into the formula:

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Height 168 m3 / 28 m2

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Step 3: Perform the division:

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Height 6 meters (m)

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This calculation shows that the height of the cuboid is 6 meters.

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Verification Process

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To verify the solution, we can use the formula for the volume of a cuboid and confirm that the volume is indeed 168 m3 when the height is 6 m and the base area is 28 m2.

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Verification Step 1: Calculate the Volume using the derived height:

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Volume Base Area × Height 28 m2 × 6 m 168 m3

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The verification shows that the volume matches the given value, validating the solution.

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Summary and Application

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By using the basic formula relating the volume and base area of a cuboid, we can accurately determine the height of the cuboid. This method is widely applicable in various fields, such as construction, packaging design, and scientific research.

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Understanding these relationships and being able to apply them practically is crucial for solving real-world problems involving three-dimensional shapes.