Question

If you were filling the cylinder up with water using a cone that has the same height and diameter, how many cones will it take to fill up the cylinder?

Answer 1

It required 3 cones to fill up the cylinder with the same height and diameter.

Explanation:

Let the radius of the cone and cylinder be r.

Let the height of the cone and cylinder be h.

As we know that
`\text{Volume of cylinder}=\pi r^2h` ....(1)

`\text{Volume of cone}=(1)/(3)\pi r^2h`

It can be observed that the volume of a cone is
`(1)/(3)`rd the volume of the cylinder. so, multiply the volume of the cone by 3.

`3 * \text{Volume of cone}=3 * (1)/(3)\pi r^2h`

`3 * \text{Volume of cone}= \pi r^2h`

`3 * \text{Volume of cone}= \text{Volume of cylinder}` (From equation 1 )

Hence, It required 3 cones to fill up the cylinder with the same height and diameter.