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:
Answer & explanation
Correct answer: option 2
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.