Supposed to spare of a cone share the same radius, and the height of the cone is twice the radius which ratio describes the ship between the formulas for the volume of a cone to the volume of spare one point
The volume ratio between a cone and a sphere can be described by the following ratio:
Volume of Cone : Volume of Sphere
(Vcone) : (Vsphere)
To find the volume of a cone, we use the formula:
Vcone = (1/3) * π * r^2 * h
where r is the radius and h is the height.
In this case, the height of the cone is twice the radius, so h = 2r. Substituting this into the volume formula, we get:
Vcone = (1/3) * π * r^2 * (2r)
Simplifying this equation, we have:
Vcone = (2/3) * π * r^3
To find the volume of a sphere, we use the formula:
Vsphere = (4/3) * π * r^3
Now we can compare the volume of the cone to the volume of the sphere:
Vcone : Vsphere
= [(2/3) * π * r^3] : [(4/3) * π * r^3]
= (2/3) : (4/3)
= 2 : 4
= 1 : 2
Therefore, the ratio of the volume of a cone to the volume of a sphere in this case is 1 : 2.