Hemisphere of diameter 2 cm — difference (TSA − CSA): For a hemisphere with diameter 2 cm (radius 1 cm), find the difference between its total surface area and its curved surface area.

Introduction / Context:For a hemisphere, the total surface area (TSA) includes the curved area plus the area of the flat circular base, while the curved surface area (CSA) excludes the base. Their difference is exactly the base area.

Given Data / Assumptions:

• Diameter = 2 cm ⇒ r = 1 cm.
• TSA (hemisphere) = 3πr^2.
• CSA (hemisphere) = 2πr^2.

Concept / Approach:Compute TSA − CSA = (3πr^2 − 2πr^2) = πr^2 = π for r = 1.

Step-by-Step Solution:TSA − CSA = πr^2 = π * 1^2 = π cm2

Verification / Alternative check:Geometrically, this is just the area of the base circle, which must be πr^2.

Why Other Options Are Wrong:2π, 3π, 4π correspond to 2, 3, 4 times the base area and do not apply to the difference.

Common Pitfalls:Using diameter instead of radius in the circle area formula; mixing TSA with CSA expressions.

Final Answer:π sq cm