The height of a right circular cone is 35 cm and the area of its curved surface is four times the area of its base. What is the volume of the cone (in $10^{-3} m^3$ and correct up to three decimal places)?

2.994

We know that,

Volume of cone = \(\frac{1}{3}\) πr²h

Curved surface area of cone = πrl

Base area of cone = πr²

We are given,

Height of the cone h = 35 cm            

So, 4 × πr² = πrl

l = 4r

We also know, l² = r² + h²

(4r)² = r² + 35²

16r² – r² = 1225

15r² = 1225

r² = \(\frac{1225}{15}\)

Volume of the cone = \(\frac{1}{3}\) × \(\frac{22}{7}\) × \(\frac{1225}{15}\) × 35 = 2994 cm³ or 2.994