$3\mathrm{.}3$ You are a virtualization and cloud computing architect working for a large multinational corporation. The company has decided to modernize its IT infrastructure by adopting cloud computing technologies and implementing virtualization solutions.

Your role is to design and implement a cloud computing architecture that leverages virtualization to enhance scalability, efficiency, and cost$-$effectiveness across the organization's diverse range of business operations. Explain the role of virtualization in cloud computing architecture and its significance in modernizing IT infrastructure. Describe at least three types of virtualization technologies commonly used in cloud environments and their respective benefits in terms of resource optimization, workload management, and infrastructure agility. $(25$ Marks$)$