What is the extracts volume of the largest cone that can fit into a cube with edges of 10 inches

Volume of a cone = π r² h/3

I envisioned a cone inside a cube. I only identified the necessary value to compute for the exact volume of the largest cone.

Edges of the cube is 10 inches. When the circle part of the cone is placed in the circle, the diameter would be 10 inches also. I divided it by 2 to get the value of the radius, resulting to 5 inches.

The height of the cone is also the height of the cube. Thus, it is 10 inches.

Volume of the cone = 3.14 * (5in)² * 10in/3
V = 3.14 * 25in² * 3.33 in
V = 261.405 in³ or 261.41 in³  VOLUME OF THE LARGEST CONE THAT CAN FIT IN A 10 INCH CUBE