A right circular cone has slant height 10 m and vertical height 8 m. What is the area of its curved (lateral) surface?

Problem Restatement

Compute the lateral surface area (CSA) of a cone given its slant height and vertical height.

Given data

• Slant height, l = 10 m
• Vertical height, h = 8 m

Concept / Formulae

• Radius from Pythagoras: r = √(l^2 − h^2)
• Curved surface area: CSA = πr l

Step-by-step calculation

r = √(10^2 − 8^2) = √(100 − 64) = √36 = 6 mCSA = π × 6 × 10 = 60π m^2 ≈ 188.50 m^2

Final Answer

Curved surface area = 60π m^2 (≈ 188.5 m^2).