SmarterEd

Aussie Maths & Science Teachers: Save your time with SmarterEd

Volume, SM-Bank 065

  1. Given the triangular face of the prism above is isosceles, use Pythagoras' Theorem to calculate its perpendicular height. Give your answer correct to the nearest whole centimetre.  (2 marks)
  2. Using your answer from (a), calculate the volume of the prism in cubic centimetres.  (2 marks)
Show Answers Only

a.    \(7\ \text{cm}\)

b.    \(168\ \text{cm}^3\)

Show Worked Solution
a.    \(a^2+b^2\) \(=c^2\)
  \(a^2+3^2\) \(=7.6^2\)
  \(a^2\) \(=7.6^2-3^2\)
  \(a^2\) \(=48.76\)
  \(a\) \(=\sqrt{48.76}=6.982\dots\)
  \(a\) \(\approx 7\)

 
\(\therefore\ \text{The perpendicular height of the triangle is }7\ \text{cm, (nearest whole centimetre).}\)
 

b.    \(V\) \(=Ah\)
    \(=\Big(\dfrac{1}{2}\times 6\times 7\Big)\times 8\)
    \(=21\times 8\)
    \(=168\ \text{cm}^3\)