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
\(32cm^3\)
Verified Correct Answer: B.
Step-by-Step Mathematical Solution
\(BD^2 = 4^2 + 4^2\)
\(BD = \sqrt{16 + 16} = \sqrt{32}\)
\(BD = 4\sqrt{2} cm\)
\((2\sqrt{3})^2 = (2\sqrt{2})^2 + h^2\)
\(h^2 = 12 - 8 = 4\)
\(h = \sqrt{4} = 2 cm\)
Volume of pyramid = \(\frac{a^2 h}{3}\)
= \(\frac{4^2 \times 2}{3}\)
= \(\frac{32}{3} = 10\frac{2}{3} cm^3\)
Source: Myschool Past Questions Archive (Record #26512)