Suppose a sphere , cylinder, and cone all share the same radiusThe cylinder and cone also share the same height, which is twice the radiusWhich of the following is true about the relationship between the volume formulas for the sphere , cylinder , and cone ? (point)
The volume formulas for the sphere, cylinder, and cone are given by:
Sphere: V = (4/3)πr³
Cylinder: V = πr²h
Cone: V = (1/3)πr²h
where r is the radius and h is the height.
In this case, the radius is the same for all three shapes, and the height of the cylinder and cone is twice the radius.
We can compare the volume formulas as follows:
Volume of sphere: V_sphere = (4/3)πr³
Volume of cylinder: V_cylinder = πr²(2r) = 2πr³
Volume of cone: V_cone = (1/3)πr²(2r) = (2/3)πr³
Therefore, the relationship between the volume formulas for the sphere, cylinder, and cone is:
Volume of sphere < Volume of cylinder < Volume of cone.