the volume of the cone is 25 The volume of the sphere if the radius is the same value as the cone.

Answer 1

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.