Question

if the cylinder and cone are the same radius and height then how many cones full of milk can fill the cylinder? answer with reason s

Answer 1

let H be the height of the cylinder and of the cone
let r be the radius of cylinder and cone
let n be the number of cones that can be fill the cylinder
then,
n x volume of cones=volume of cylinder
n x1/3 (pir^2H)=pir^2H
n=3
Hence 3 cones should be filled the cylinder.

Answer 2

If a cone of same radius, height is created from a cylinder, then Volume of cylinder = 3 * Volume of cone.

From this, We could say 3 cones full of milk would fill the cylinder.

Volume of a cone with radius r, height h is given by

$V = \frac{1}{3} \pi {r}^{2} h$

Volume of a cylinder with radius r, height h is given by

$v = \pi {r}^{2} h$

Let's say x cones of milk can fill the cylinder.

So v = xV

$\pi {r}^{2} h = x( \frac{1}{3} \pi {r}^{2} h ) \\ \\ \frac{ \pi {r}^{2} h }{ \pi {r}^{2} h } = \frac{x}{3} \\ \\ 1 = \frac{x}{3} \\ \\ x = 3$

Therefore, If the cylinder and cone has same radius and height, then 3 cones of milk can fill the cylinder.