Suppose a sphere, cylinder, and cone all share the same radius and the cylinder and cone also share the same he twice the radius. Which of the following is true about the relationship between the volume formulas for the sphere, c cone? (1 point)
The volume formulas for a sphere, cylinder, and cone are as follows:
Sphere: V = (4/3)πr³
Cylinder: V = πr²h
Cone: V = (1/3)πr²h
Given that the radius is the same for all three shapes, we can let the radius be represented by "r". If the cylinder and cone share the same height, which is twice the radius (2r), we can now substitute these values into the equations:
Sphere: V = (4/3)πr³
Cylinder: V = πr²(2r) = 2πr³
Cone: V = (1/3)πr²(2r) = (2/3)πr³
Comparing the volume formulas for the sphere and cone, we can see that the volume of the cone, (2/3)πr³, is two-thirds the volume of the sphere, (4/3)πr³. Therefore, the cone's volume is two-thirds of the sphere's volume.
The statement that is true about the relationship between the volume formulas for the sphere and cone is: The volume of the cone is two-thirds the volume of the sphere.