Question

A cylindrical rod of length $h$ is melted and cast into a cone of base radius twice that of the cylinder. What is the height of the cone?

• A. $\frac{3h}{4}$
• B. $\frac{4h}{3}$
• C. $2$
• D. $\frac{h}{2}$

Answer 1

The correct option is A $\frac{3h}{4}$

$r_{cone}=2r_{cyl}.$ & $V_{cone}=V_{cyl}.$

$\Rightarrow \frac{\pi }{3}{r}^2$ cone have $=\pi r^{2}cylh\Rightarrow hcone=3h{\left(\frac{r_{cyl}}{r_{cone}}\right)}^2$

$\Rightarrow hcone=\frac{3h}{4}$