suppose a sphere cylinder and cone all share the same radius the cylinder and cone also share the same height which is twice the radius which if the following is true abiut 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 relationship between the volume formulas for the sphere, cylinder, and cone is as follows:
- The volume of a sphere with radius "r" is given by the formula V_sphere = (4/3)πr^3.
- The volume of a cylinder with radius "r" and height "h" is given by the formula V_cylinder = πr^2h.
- The volume of a cone with radius "r" and height "h" is given by the formula V_cone = (1/3)πr^2h.
In this scenario, the cylinder and cone share the same height, which is twice the radius. Therefore, the height of both the cylinder and cone is 2r.
Since all three shapes have the same radius, we can represent it as "r" for simplicity.
Hence, for the given scenario, the relationship between the volume formulas can be expressed as follows:
V_sphere : V_cylinder : V_cone
= (4/3)πr^3 : πr^2(2r) : (1/3)πr^2(2r)
On simplifying this expression, we get:
V_sphere : V_cylinder : V_cone
= (4/3)πr^3 : 2πr^3 : (2/3)πr^3
= (4/3) : 2 : (2/3)
Therefore, the relationship between the volume formulas for the sphere, cylinder, and cone in this scenario is:
Volume of Sphere : Volume of Cylinder : Volume of Cone
= (4/3) : 2 : (2/3)