Question 1187680
the direct variation formula is y = k * x


when x = r^2, the formula becomes y = k * r^2.


when r = 3 and y = 36 * pi, the formula becomes 36 * pi = k * 3^2


simplify to get 36 * pi = k * 9


solve for k to get k = 36 * pi / 9 = 4 * pi.


now that you have the value of k, you can solve for y when r = 5.


the formula of y = k * r^2 becomes y = 4 * pi * 5^2 which becomes y = 4 * pi * 25 which becomes y = 100 * pi.


k, being the constant of variation, doesn't change, as long as you're dealint with the surface area of a sphere.


if you look up the formula for the surface area of a sphere, you will find that the formula is y = 4 * pi * r^2, where y is the surface area of the sphere.
4 * pi remains the same, regardless of the measure of the radius.
it becomes the constant of variation in that formula.