the volume of the cone is 25 The volume of the sphere if the radius is the same value as the cone.
To find the volume of the sphere with the same radius as the cone, we first need to find the radius of the cone. The formula for the volume of a cone is:
V_cone = (1/3)πr^2h
Given that the volume of the cone is 25 and the formula for the volume of a cone, we can set up the following equation:
25 = (1/3)πr^2h
Since we know the volume of the cone is 25, we can solve for h:
25 = (1/3)πr^2h
75 = πr^2h
h = 75/(πr^2)
Now that we have h in terms of r, we can substitute this value into the formula for the volume of a sphere:
V_sphere = (4/3)πr^3
Substitute h into the volume formula for the cone:
25 = (1/3)πr^2(75/(πr^2))
25 = 25
1 = 1
Since 1=1, the volume of the sphere with the same radius as the cone is also 25.