Correct Answer: 3072

Solution : Given: Total surface area of pyramid = 1536 m ²
Area of base = 37.5% of total surface area
= $\frac{37.5}{100}\times1536$
= $\frac{3}{8}\times1536$
= $576$
Remaining area = 1536 – 576 = 960
$\therefore$ lateral surface area = 960 m ²
Area of square base = 576
⇒ $\text{side}^2=576$
$\therefore \text{side}=24$
Perimeter of base = 4 × 24 = 96
We know that,
Lateral surface area of pyramid = $\frac{1}{2}$ × perimeter of base × slant height
⇒ $960 = \frac{1}{2} \times 96\times$ slant height
$\therefore$ Slant height = 20
$\text{Height} = \sqrt{\text{slant height}^2-(\frac{\text{side}}{2})^2}$
= $\sqrt{20^2-12^2}$
= $16$
Now, Volume of pyramid = $\frac{1}{3}$ × area of base × height
= $\frac{1}{3}\times576\times16$
= $3072$ m ³
Hence, the correct answer is 3072.