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Find the height of the cuboid whose base area is \[180c{m^2}\] and volume is \[900c{m^3}\]?

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Last updated date: 13th Jun 2024
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Answer
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Hint:
Volume of a cuboid can be expressed as \[V = (l \times b \times h)\]. But we know that \[area = l \times b\]. So, we get our simplified formula of Volume of a cuboid =\[area \times height\]. The base area and volume are given to us in the question, so we will use these values to calculate the height of the cuboid.

Complete step by step solution:
Cuboid is a solid box whose every surface is a rectangle of the same area or different areas. A cuboid will have a length, breadth and height. Hence, we can conclude that volume is 3 dimensional. To measure the volume, we need to know the measure of the 3 sides. Since volume involves 3 sides it is measured in cubic units.
Volume of a cuboid = \[(length \times breadth \times height)unit{s^3}\]
\[V = (l \times b \times h)\]
Since, \[area = l \times b\]
Volume of a cuboid =\[area \times height\]
We have been given the base area of the cuboid and the volume of the cuboid.
We can substitute this in the equation above and solve it for height and we will get the required answer.
\[
  Volume = area \times height \\
   \Rightarrow 900 = 180 \times height \\
   \Rightarrow height = \dfrac{{900}}{{180}} \\
   \Rightarrow height = 5cm \\
\]

Hence, the required height is $5cm$.

Note:
This question is fairly simple since it is the case of a cuboid. An easy application of the above method will be to cubes where all the sides are equal. If you find the square root of the base area in the case of a cube, you will find the height of the cube automatically. Complications might arise in case of cones, where there are two surface areas. You might have to calculate the slant height in order to calculate the height from the volume.