suppose a 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 is as follows:
1. Sphere: The volume of a sphere is given by the formula V = (4/3)πr^3, where r is the radius.
2. Cylinder: The volume of a cylinder is given by the formula V = πr^2h, where r is the radius and h is the height.
3. Cone: The volume of a cone is given by the formula V = (1/3)πr^2h, where r is the radius and h is the height.
In this case, since the cylinder and cone share the same height (twice the radius), the height (h) in both formulas is the same.
Therefore, the relationship between the volume formulas for the sphere, cylinder, and cone, in terms of the radius (r) and the height (h), is:
Volume of sphere : Volume of cylinder = (4/3)πr^3 : πr^2h
Volume of sphere : Volume of cone = (4/3)πr^3 : (1/3)πr^2h
Simplifying these equations, we get:
Volume of sphere : Volume of cylinder = 4r : h
Volume of sphere : Volume of cone = 4r : h/3