Correct Answer: 960 cm ³

Solution : Given: Length of the diagonal of the square = $24\sqrt2$
Let the side of the square be $a$.
We know that,
Length of the diagonal of the square = $a\sqrt2$
Thus, $24\sqrt2=a\sqrt2$
$\therefore a = 24$ cm
Perimeter of square = 24 × 4 = 96 cm
Area of the square = 24 × 24 = 576 cm ²
Given: Lateral surface area of pyramid = 624 cm ²
We know that,
Lateral surface area of pyramid = $\frac{1}{2}$ × perimeter of base × slant height
⇒ $624 = \frac{1}{2}×96$ × slant height
$\therefore$ Slant height = $\frac{624\times2}{96}= 13$ cm
Now, Height = $\sqrt{\text{slant height}^2-{(\frac{\text{side of square}}{2}})^2}$
= $\sqrt{13^2-12^2}$
= $\sqrt{169-144}$
= $5$ cm
Volume of the pyramid = $\frac{1}{3}$× area of base × height
= $\frac{1}{3}\times576\times5$
= $960$ cm ³
Hence, the correct answer is 960 cm ³ .