To find the volume of a spring, the formula used is (π*d²/4) * π*D*Nt, where Nt represents the number of turns. The instructor specified that the volume of a cylinder method is not applicable for this problem. Key design goals for springs under static loading include the spring constant, material suitability for environmental conditions, and dimensions. Additionally, considerations like free height, solid height, working height, and stress relaxation are crucial for static springs. Understanding these factors is essential for effective spring design.