A right pyramid is on a square base of side 4cm. The slanting side of the pyramid is \(2\sqrt{3}\) cm. Calculate the volume of the pyramid

  • A \(5\frac{1}{3}cm^3\)
  • B \(10\frac{2}{3}cm^3\)
  • C \(16cm^3\)
  • D \(32cm^3\)
waec 2002mathematics

The correct answer is B. \(10\frac{2}{3}cm^3\)

\(BD^2 = 4^2 + 4^2\)

\(BD = \sqrt{16 + 16} = \sqrt{32}\)

\(BD = 4\sqrt{2} cm\)

\((2\sqrt{3})^2 = (2\sqrt{2})^2 + h^2\)

\(h^2 = 12 - 8 = 4\)

\(h = \sqrt{4} = 2 cm\)

Volume of pyramid = \(\frac{a^2 h}{3}\)

= \(\frac{4^2 \times 2}{3}\)

= \(\frac{32}{3} = 10\frac{2}{3} cm^3\)

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