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Volume, SM-Bank 133

The figure below is a prism with a parallelogram as the uniform cross-section.

Calculate the value of \(x\), the perpendicular height of the cross-section, given the volume of the prism is 2880 cubic millimetres.  (2 marks)

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\(12\ \text{mm}\)

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\(\text{The uniform cross-section is a parallelogram.}\)

\(\therefore\ A\) \(=b\times h\)
  \(=10\times x\)
  \(=10x\ \text{mm}^2\)

 

\(V\) \(=A\times h\)
\(2880\) \(=10x\times 24\)
\(2880\) \(=240x\)
\(\therefore\ x\) \(=\dfrac{2880}{240}\)
  \(=12\ \text{mm}\)