Question

The base edges and lateral edges of a square pyramid are equal. If the base edge is 6 cm then the volume of the pyramid is :

• A. 108 cu.cm
• B. 108√2 cu.cm
• C. 36 cu.cm
• D. 36√2 cu.cm

Answer 1

Answer:

D. 36√2 cu.cm

$V = \frac{a^3\sqrt2}{6}=\frac{6^3\sqrt2}{6}=36\sqrt2$

$V=\frac{1}{3}Ah=\frac{1}{3}a^2h$

$h=\sqrt{a^2-(\frac{a\sqrt2}{2})^2}$

$=\sqrt{a^2-\frac{a^2}{2}}$

$h=\frac{a}{\sqrt2}$

$v=\frac{1}{3}a^2\frac{a}{\sqrt2}=\frac{a^3}{3\sqrt2}$