SmarterEd

Aussie Maths & Science Teachers: Save your time with SmarterEd

Volume, SM-Bank 134

The figure below is a prism with a kite 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 1485 cubic centimetres.  (2 marks)

Show Answers Only

\(11\ \text{cm}\)

Show Worked Solution

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

\(\therefore\ A\) \(=\dfrac{1}{2}\times x\times y\)
  \(=\dfrac{1}{2}\times x\times 18\)
  \(=9x\ \text{cm}^2\)

 

\(V\) \(=A\times h\)
\(1485\) \(=9x\times 15\)
\(1485\) \(=135x\)
\(\therefore\ x\) \(=\dfrac{1485}{135}\)
  \(=11\ \text{cm}\)