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.
Accepted Solution
A:
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.