The perceptron is a linear classifier that separates the data, in any dimension, through hyper planes. If the dimension is $2,$ for example, the perceptron uses lines in R$2$ to perform the classification.

Part A: Instead of a cube, consider a sphere with radius $=2$ and center at $(0,0,0).$ Explain why a perceptron would not be an optimum method in the case of a sphere.

Part B: Consider a hypothetical case where you had to use a perceptron with a sphere. Explain how you would solve the problem, including the design of the perceptron with your answer.