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Measurement, STD2 EQ-Bank 14 MC

A square pyramid has a volume of 384 cm³ and a perpendicular height of 8 cm.

 Calculate the side length of the square base. Use the formula \(V = \frac{1}{3}Ah\) where \(A\) is the area of the base.

  1. 8 cm
  2. 12 cm
  3. 16 cm
  4. 24 cm
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\(B\)

Show Worked Solution
\(V\) \(=\frac{1}{3}Ah\)
\(384\) \(=\frac{1}{3}\times A\times 8\)
\(384\) \(=\dfrac{8A}{3}\)
\(8A\) \(=384\times 3=1152\)
\(A\) \(=\dfrac{1152}{8}\)
  \(=144\ \text{cm}^2\)
\(\text{Since the base is a square: }x^2\) \(=144\)
\(x\) \(=\sqrt{144}\)
  \(=12\ \text{cm}\)

 

\(\Rightarrow B\)