Question

A cylindrical rod of lenght h is meted 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. $\frac{4h}{4}$
• C. 2h
• D. $\frac{h}{2}$

Answer 1

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

Let the radius of cylindrical rod is r and cylindrical rod height is h given

Then volume of cylindrical rod=$\pi r^{2}h$

And volume of cone of base twice the radius of cylindrical rod=$\frac{1}{3}\pi (2r{)}^{2}H=\frac{4}{3}\pi r^{2}H$

The cylindrical rod melted and make cone

$\therefore \frac{4}{3}\pi r^{2}H=\pi r^{2}h\Rightarrow H=\frac{3h}{4}$