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)?
Answer & explanation
Correct answer: option 1
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