Question

A cone is placed in the cube with the same diameter and height as the side of s. The diameter and height of this cone are equal to the side length, s, of the cube in which the cone is inscribed. What is the equation for the cone's volume?

1) a
2) b
3) c
4) d

Answer 1

The equation for the volume of a cone inscribed in a cube, with both diameter and height equal to the cube's side length s, is V = (1/12)\(\pi s^{3}).

Step-by-step explanation:

To find the equation for the volume of a cone with its diameter and height equal to the side s of the cube, we will use the formula for the volume of a cone, which is V = (1/3)\(\pi r^{2}h). Given that the diameter of the cone is equal to its height and also to the side of the cube, the radius r is half the side length, or s/2. Consequently, substituting s/2 for r and s for h, we get the equation V = (1/3)\(\pi (s/2)^{2}s), which simplifies to V = (1/12)\(\pi s^{3}).