Question

Katherine is using a cone to fill a cylinder with sand. If the radii and height are equal on both objects, and Katherine fills the cone to the very top, how many cones will it take to fill the cylinder with sand? Complete the explanation. It will take cones to fill the cylinder with sand. Because the volume formula for a cylinder is V = πr2h, and the volume formula for a cone is V = 1 πr2h, the volume of a cone is 1 the volume of the cylinder.

Answer 1

It will take 3 cones to fill up the cylinder.

Because the formula for the volume of a cylinder is V = πr²h, and the formula for the volume of a cone is V = 1/3πr²h, the volume of the cone is 1/3 the volume of the cylinder. Therefore it takes 3 cones to fill up the cylinder.

Answer 2

3 cones will take it to fill the cylinder with sand.

Explanation:

Given Radius and height of the cone and cylinder are equal.

We have to tell how many cones can fill the cylinder.

To fill the sand in the cylinder and cone.

We use concept of volume.

Volume of cylinder = πr²h

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

let n be number of cones required to fill the cylinder.

According to the question,

n × volume of cone = volume of cylinder

`n*(1)/(3)\pi r^2h=\pi r^2h`

`n=\pi r^2h*(3)/(\pi r^2h)`

`n=3`

Therefore, 3 cones will take it to fill the cylinder with sand.