Please someone explain to me how they got the answer. I’m so confused

Question

The volume of a cone varies jointly as the square of its radius and its height. If the volume of a cone is 25π cubic inches when the radius is 5 inches and the height is 3 inches, find the volume of a cone when the radius is 3 inches and the height is 6 inche

Answer 1

When A varies jointly as B and C then we say A is proportional to B times C or, A = k*B*C where k is the constant of proportionality.

So when they say (volume) varies jointly as (the square of radius) and (height) then we can say V = k*r²*h

But V = 25π when r = 5 and h = 3. Plugging those values into our V = k*r²*h equation we get 25π = k*5²*3 or 25π = 75k then dividing both sides by 75 we get k = π/3

Now we know k so we can write our equation as V = π/3*r²*h

We can now solve for volume if r = 3 and h = 6

V = π/3*(3)²*(6) = 18π cubic inches