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Volume, SM-Bank 010

A rectangular block of land has width 50 metres and length 85 metres.

In order to build a house, the builders dig a hole in the block of land.

The hole has the shape of a right-triangular prism,  \(ABCDEF\).

The width \(AD\) = 20 m, length \(DC\) = 25 m and height \(EC\) = 4 m are shown in the diagram below.
 

Calculate the volume of the right-triangular prism, \(ABCDEF\), giving your answer in cubic metres.  (2 marks)

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\(1000\ \text{m}^3\)

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\(\text{Cross-section is a triangle}\)

\(A\) \(=\dfrac{1}{2}\times bh\)
  \(=\dfrac{1}{2}\times 25\times 4\)
  \(= 50\ \text{m}^2\)

 

\(\therefore\ V\) \(=50\times 20\)
  \(=1000\ \text{m}^3\)

Filed Under: Prisms Tagged With: num-title-ct-core, smc-4980-10-Triangular

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