Question

A pyramid is formed by cutting off a corner of a cube whose edge is two metres by a plane which bisects its three co-terminus edges. The 'volume of the pyramid is

• A. $1m^3$
• B. $\frac{1}{2}{m}^3$
• C. $\frac{1}{3}{m}^3$
• D. $\frac{1}{6}{m}^3$

Answer 1

The correct option is D $\frac{1}{6}{m}^3$

OA $=$ OB $=$ OC $=$ 1
AB $=$ BC $=$ CA $=\sqrt{2}$
AQ $=\sqrt{2}sin{60}^{\circ }$
$=\sqrt{\frac{3}{2}}$
AP $=\frac{2}{3}.\frac{\sqrt{3}}{2}=\frac{\sqrt{2}}{3}$
and $OP=O{A}^2-A{P}^2=\frac{1}{3}$
$\therefore$ Required volume
$=\frac{1}{3}\times Areaof\Delta ABC\times OP$
$=\frac{1}{6}{m}^3$