Question

solid cylinder is melted and recast into a cone of same radius the height of the cone and cylinder are in the ratio​

Answer 1

Answer:

h:h/3

Step-by-step explanation:

PI×r^2H:1/3PI×R^2×H=H:H/3

Answer 2

The ratio of height of cone and cylinder = 3 : 1.

Step-by-step explanation:

Let the radius of cylinder = r = The radius of cone and

The height of cylinder = h

The height of cone = H

To find, the ratio of height of cone and cylinder = ?

We know that,

The volume of cylinder =$\pi r^{2} h$

The volume of cone =$\dfrac{1}{3} \pi r^{2} H$

∴ The ratio of height of cone and cylinder

=$\dfrac{1}{3} \pi r^{2} H$ :$\pi r^{2} h$

= $\dfrac{H}{3}:h$

⇒ $\dfrac{H}{h}$ = 3 : 1

Thus, the ratio of height of cone and cylinder = 3 : 1.