The curved surface area of a cone is 308 cm² and its slant height is 14 cm. Find

1. (i) the radius of the base,
2. (ii) the total surface area of the cone.

Step-by-step solution

Idea: Solve πrl = 308 for r, then add the base πr² to the curved surface.

Check: πr(l + r) = 227 × 7 × 21 = 22 × 21 = 462 ✓.

Answer to write in the exam

Common mistakes that cost marks

• Recalculating the curved surface wrongly instead of using the given 308 cm².
• Adding 2πr² (two bases); a cone has one base.

How this can come in the exam

Try one yourself

The curved surface area of a cone is 616 cm² and its slant height is 14 cm. Find its radius and total surface area. (π = 227)

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