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

A.
(5frac{1}{3}cm^3) 
B.
(10frac{2}{3}cm^3) 
C.
(16cm^3) 
D.
(32cm^3)
Correct Answer: Option B
Explanation
(BD^2 = 4^2 + 4^2)
(BD = sqrt{16 + 16} = sqrt{32})
(BD = 4sqrt{2} cm)
((2sqrt{3})^2 = (2sqrt{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} = 10frac{2}{3} cm^3)