Calculate total and curved surface area
Step 1: Determine the Radius
Measure r from the center to the curved surface (or from center to flat base edge).
Why: The hemisphere has two surfaces (curved and flat); radius is needed for both.
Step 2: Verify Positive Radius
Ensure r > 0; zero or negative radius is invalid.
Why: Geometric solids require positive dimensions.
Step 3: Calculate Curved Surface Area
Use A_curved = 2πr² (half of a full sphere’s surface area 4πr²).
Why: The curved part is exactly half the sphere; dividing the sphere formula by 2 yields this.
Step 4: Calculate Flat Base Area
Use A_base = πr² (area of a circle with radius r).
Why: The hemisphere has a flat circular base; its area is the full circle formula.
Step 5: Total and Verify
Total SA = 2πr² + πr² = 3πr². Verify it equals three-halves of a full sphere.
Why: This confirms the calculation accounts for both the curved and flat surfaces.
Curved Surface Area: 2πr²
Base Area: πr²
Total Surface Area: 3πr² (Curved + Base)
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