The radius and height of a right circular cone are in the ratio 3 : 4. If its volume is $$301\frac{5}{7}$$ cm³, what is its slant height ?

Solution(By Examveda Team)

Let the radius and height of the cone be 3x and 4x respectively
Then,
$$\eqalign{ & \frac{1}{3} \times \frac{{22}}{7} \times {\left( {3x} \right)^2} \times 4x = \frac{{2112}}{7} \cr & \Rightarrow \frac{{264}}{7}{x^3} = \frac{{2112}}{7} \cr & \Rightarrow {x^3} = \frac{{2112}}{{264}} \cr & \Rightarrow {x^3} = 8 \cr & \Rightarrow x = 2 \cr} $$
∴ Radius = 6 cm, Height = 8 cm
Slant height :
$$\eqalign{ & = \sqrt {{6^2} + {8^2}} \,cm \cr & = \sqrt {100} \,cm \cr & = 10\,cm \cr} $$