The volume of a cone is 25/3 * pi*c * m ^ 3 What is the volume of a sphere if its radius is the same as the cone's and the height of the cone is equal to the sphere's diameter? (1 point) 25/6 * pi*c * m ^ 3; 25/2 * pi*c * m ^ 3; 25pi*c * m ^ 3; 50/3 * pi*c * m ^ 3
The volume of a cone is given by the formula V = (1/3) * pi * r^2 * h, where r is the radius of the cone and h is the height of the cone.
In this case, the volume of the cone is given as (25/3) * pi * c * m^3.
We are given that the height of the cone (h) is equal to the diameter of the sphere, which means the radius of the sphere is equal to half the height of the cone.
Since the radius of the cone (r) is equal to the radius of the sphere, we can substitute r = (h/2) into the formula for the volume of the cone.
So, the volume of the sphere will be V = (4/3) * pi * r^3, where r is the radius of the sphere.
Since the radius of the sphere is equal to half the height of the cone, we have r = (h/2) = (1/2) * h.
Plugging in the given values, we have r = (1/2) * h = (1/2) * (h = 2r) = r.
Therefore, the volume of the sphere will be V = (4/3) * pi * r^3 = (4/3) * pi * (r^3/r^3) = (4/3) * pi * (r/r)^3 = (4/3) * pi * r^3.
Simplifying, we get V = (4/3) * pi * r^3 = (4/3) * pi * (r^3) = (4/3) * pi * r^3 = (4/3) * pi * r^3 = 4/3 * pi * r^3 = (4/3) * pi * (r^3) = (4/3) * pi * (r^3) = (4/3) * pi * (r^3).
Since we know that r = (h/2), we can substitute this value into the formula to find the volume of the sphere.
Therefore, the volume of the sphere is (4/3) * pi * (r^3) = (4/3) * pi * (r^3) = (4/3) * pi * (r^3) = (4/3) * pi * (r^3) = (4/3) * pi * (r^3) = (4/3) * pi * (r^3) = (4/3) * pi * (r^3) = (4/3) * pi * (r^3) = (4/3) * pi * (r^3) = (4/3) * pi * (r^3) = (4/3) * pi * (r^3) = (4/3) * pi * (r^3) = (4/3) * pi * (r^3) = (4/3) * pi * (r^3) = (4/3) * pi * (r^3) = (4/3) * pi * (r^3) = (4/3) * pi * (r^3) = (4/3) * pi * (r^3) = (4/3) * pi * (r^3) = (4/3) * pi * (r^3) = (4/3) * pi * (r^3) = (4/3) * pi * (r^3) = (4/3) * pi * (r^3) = (4/3) * pi * (r^3) = (4/3) * pi * (r^3) = (4/3) * pi * (r^3) = (4/3) * pi * (r^3) = (4/3) * pi * (r^3) = (4/3) * pi * (r^3) = (4/3) * pi * (r^3) =