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Volume, SM-Bank 066

Gavin is going camping in the summer holidays and purchased the two-person tent shown below.

  1. Given the triangular face of the tent is isosceles, use Pythagoras' Theorem to calculate the perpendicular height of the tent.  (2 marks)
  2. Using your answer from (a), calculate the volume of the tent in cubic metres.  (2 marks)
  3. What is the capacity of the tent in litres?  (1 mark)
Show Answers Only

a.    \(2\ \text{m}\)

b.    \(12 \text{m}^3\)

c.    \(12\ 000\ \text{L}\)

Show Worked Solution
a.    \(a^2+b^2\) \(=c^2\)
  \(x^2+1.5^2\) \(=2.5^2\)
  \(x^2\) \(=2.5^2-1.5^2\)
  \(x^2\) \(=4\)
  \(x\) \(=\sqrt{4}=2\)

 
\(\therefore\ \text{The perpendicular height of the tent is }2\ \text{metres.}\)
 

b.    \(V\) \(=Ah\)
    \(=\Big(\dfrac{1}{2}\times 3\times 2\Big)\times 4\)
    \(=3\times 4\)
    \(=12\ \text{m}^3\)

 

c.    \(1\ \text{m}^3\) \(=1000\ \text{L}\)
  \(\therefore\ 12\ \text{m}^3\) \(=12\ 000\ \text{L}\)

  
\(\therefore\ \text{The capacity of the tent is }12\ 000\ \text{litres.}\)