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Volume, SM-Bank 135

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

Calculate the value of \(x\), the length of the diagonal in the cross-section, given the volume of the prism is 1950 cubic metres.  (2 marks)

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\(20\ \text{m}\)

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

\(\therefore\ A\) \(=\dfrac{1}{2}\times x\times y\)
  \(=\dfrac{1}{2}\times x\times 15\)
  \(=7.5x\ \text{m}^2\)

 

\(V\) \(=A\times h\)
\(1950\) \(=7.5x\times 13\)
\(1950\) \(=97.5x\)
\(\therefore\ x\) \(=\dfrac{1950}{97.5}\)
  \(=20\ \text{m}\)