\( -\sqrt{11} \) ho formula for surface area of a circular ring with an outer radius of \( R \) nor radlus of \( r \) is given as: \( A=\pi\left(R^{2}-r^{2}\right) \).

The surface area formula for a circular ring, \( A = \pi(R^2 - r^2) \), funnily illustrates how the art of subtraction can lead to beautiful results! Imagine you have a big pizza with radius \( R \) and then you scoop out a smaller one with radius \( r \). The area left is your delicious ring of crust! Perfect for those who love to eat the borders! In real-world applications, understanding the surface area of rings is super useful! Think of designing a race track or even creating a new ring-style swimming pool! By mastering this formula, architects and engineers can ensure their designs are both practical and aesthetically pleasing, proving that math isn't just numbers—it's the key to creating cool stuff in our lives!