Step 1: Types of activities in Cash Flow Statement.
- Operating activities: Core business activities like cash from customers, payments to suppliers.
- Investing activities: Relating to purchase/sale of fixed assets or investments.
- Financing activities: Relating to raising/repaying capital or loans.
Step 2: Classification of purchase of building.
Building is a fixed asset. Its purchase is an outflow of cash for investment in assets.
Step 3: Conclude.
Therefore, cash purchase of building will be classified as an investing activity.
Final Answer:
\[
\boxed{\text{Investing activity}}
\]