The base of a right pyramid is a square of side 8√2 cm and each of its slant edge is of length 10 cm. What is the volume (in cm³) of the pyramid?

Length of each side = 8√2 cm
Diagonal = √2a
= √2 × 8√2
= 16
OC $$ = \frac{{\text{d}}}{2} = \frac{{16}}{2} = 8$$
Slant edge = EC = 10 cm
In ΔOEC
EC² = OE² + OC²
10² = OE² + 8²
OE² = 6²
Height = OE = 6 cm
Volume of the pyramid
= $$\frac{1}{3}$$ × Area of base × Height
= $$\frac{1}{3}$$ × (8√2)² × 6
= 256