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
1=cone = sphere - cylinder
2=24
3=50/3
4=36
5=24
i got answers you want
The volume formula for a sphere is (4/3)πr³, where r is the radius.
The volume formula for a cylinder is πr²h, where r is the radius and h is the height.
The volume formula for a cone is (1/3)πr²h, where r is the radius and h is the height.
In this scenario, the radius of all three shapes is the same.
The height of the cylinder and cone is twice the radius, so we can substitute 2r for h in the volume formulas of both the cylinder and the cone.
Therefore, the volume formula for the cylinder becomes πr²(2r) = 2πr³, and the volume formula for the cone becomes (1/3)πr²(2r) = (2/3)πr³.
Comparing the volumes, we can see that the volume of the cylinder is twice the volume of the sphere (2πr³ vs (4/3)πr³), and the volume of the cone is (2/3) of the volume of the sphere ((2/3)πr³ vs (4/3)πr³).
So, the relationship between the volume formulas for the sphere, cylinder, and cone is that the volume of the cylinder is twice the volume of the sphere, and the volume of the cone is (2/3) of the volume of the sphere.