The volume of the cone is 25π.
The volume of the sphere if the radius is the same value as the cone.
To find the volume of the sphere, we first need to calculate the radius of the cone using the formula for the volume of a cone:
Vcone = (1/3)πr^2h
Since we know the volume of the cone is 25π, we can set this equal to the formula above and solve for the radius (r):
25π = (1/3)πr^2h
75 = r^2h
Given the volume of a cone is Vcone = (1/3)πr^2h and radius r = h, the volume of the cone can be written as Vcone = (1/3)πr^3. We can determine the radius of the cone:
25π = (1/3)πr^3
r^3 = 75
r ≈ 4.48198
Therefore, the radius of the cone is approximately 4.48198.
Next, we can calculate the volume of the sphere using the formula:
Vsphere = (4/3)πr^3
Substituting the radius we found for the cone (4.48198) into the formula:
Vsphere ≈ (4/3)π(4.48198)^3
Vsphere ≈ (4/3)π(90.413)
Vsphere ≈ 377.93π
Therefore, the volume of the sphere is approximately 377.93π.