The radius and height of a right circular cone are in the ratio 3 : 4. If its volume is 3015/7 cm3, what is its slant height ?

Answer: Option C

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