Find (i) the curved surface area and (ii) the total surface area of a hemisphere of radius 21 cm.

1. (i) the curved surface area
2. (ii) the total surface area

Step-by-step solution

Idea: Curved surface = half of the sphere’s 4πr² = 2πr². Total = curved + flat circular base πr² = 3πr².

Check: TSA − CSA = 4158 − 2772 = 1386 = 227 × 441, the area of the flat base ✓.

Answer to write in the exam

Common mistakes that cost marks

• Using 4πr² for the hemisphere.
• Adding 2πr² + 2πr² for the total; there is only one flat circle, πr².

How this can come in the exam

Try one yourself

Find the total surface area of a solid hemisphere of radius 7 cm. (π = 227)

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