Question

The radius and height of a right circular cone are in the ratio $1:2$. If its volume is $144{cm}^3$, find its slant height.

• A. 5 cm
• B. 6 cm
• C. 4 cm
• D. 5 cm

Answer 1

The correct option is B

6 cm

Volume of a cone = $\frac{1}{3}\pi r^{2}h$
Given that $\frac{r}{h}=\frac{1}{2}$
$\Rightarrow r=\frac{h}{2}$
Therefore, volume = $\frac{1}{12}\pi h^3$
Volume is given to be $144\pi {cm}^3$.
$\Rightarrow \frac{1}{12}\pi h^3=144\pi$
$\Rightarrow h^3=144\times 12$
$\Rightarrow h=12cm$
Now, slant height = $\sqrt{h^2+r^2}$
$=\sqrt{180}$
$=6\sqrt{5}cm$