Suppose sphere cylinder and cone all share the same radius, and the cylinder and cone also share the same height, which is twice the radius, which of the following is true about the relationship between the volume formulas for the sphere cylinder and cone
The relationship between the volume formulas for the sphere, cylinder, and cone can be determined by comparing their respective formulas.
The volume formula for a sphere is given by V_sphere = (4/3) * π * r^3, where r is the radius.
The volume formula for a cylinder is given by V_cylinder = π * r^2 * h, where r is the radius and h is the height.
The volume formula for a cone is given by V_cone = (1/3) * π * r^2 * h, where r is the radius and h is the height.
In this scenario, the radius is the same for all three shapes, and the height of the cylinder and cone is twice the radius. Therefore, the height of the cylinder and cone can be represented as h = 2r.
Substituting this value of h into the volume formulas for the cylinder and cone, we get:
V_cylinder = π * r^2 * (2r) = 2π * r^3
V_cone = (1/3) * π * r^2 * (2r) = (2/3) * π * r^3
Comparing the resulting volume formulas, we find that the volume of the cylinder is equal to 2π * r^3, while the volume of the cone is equal to (2/3) * π * r^3. Therefore, the volume formula for the cylinder is 3/2 times the volume formula for the cone.
In conclusion, the relationship between the volume formulas for the sphere, cylinder, and cone is that the volume formula for the cylinder is 3/2 times the volume formula for the cone.