We are given a sphere of radius r. We want to determine if there exists a cone with radius r having the same volume. Let h be the height of the cone. Let's analyze the formula for the volume of a sphere, and for the volume of a cone.
Notice that if we have a fixed r, the volume of the sphere is constant. However, the volume of the sphere depends on h and it can as small or as large as we want. This tells us that for some h, the volume of the cone can be equal to the volume of the sphere. We can also find the exact value of h for which V_\text{sphere}=V_\text{cone}.
Therefore, when h=4r — when the height of the cone is four times larger than its radius — the volume of the cone is equal to the volume of the sphere of the same radius. This makes the given statement true.
