The volume of a solid right circular cone is 600π cm³, and the diameter of its base is 30 cm. The total surface area (in cm²) of the cone is:

480π

We  know that,

The volume of cone = \(\frac{1}{3}\)πr²h

l² = r² + h²

Total surface area = πr(r + l)

We have,

The volume of cone = 600π cm³.

Diameter = 30 cm

then, the radius = r = 15 cm

The volume of cone  = \(\frac{1}{3}\) × π × 15 × 15 × h = 600π

= h = 1800 × \(\frac{1}{225}\)

= h = 8 cm

= l² = 15² + 8² = 225 + 64 = 289

= l = \(\sqrt {289}\) = 17 cm

Total surface area =  = π × 15 × (15 + 17) = π × 15 × 32 = 480π cm².